| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 6.1-a1 |
6.1-a |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{4} \) |
$3.38138$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.143358217$ |
$169.2654149$ |
1.296638683 |
\( \frac{4674618922777}{648} a^{2} + \frac{2639892313973}{162} a + \frac{3969961625285}{648} \) |
\( \bigl[a\) , \( a^{2} - 3 a - 4\) , \( 1\) , \( -45 a^{2} + 150 a + 1\) , \( 331 a^{2} - 1024 a - 289\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(-45a^{2}+150a+1\right){x}+331a^{2}-1024a-289$ |
| 6.1-a2 |
6.1-a |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$3.38138$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.071679108$ |
$169.2654149$ |
1.296638683 |
\( -\frac{4196347}{288} a^{2} - \frac{16250291}{288} a - \frac{3290287}{144} \) |
\( \bigl[a\) , \( a^{2} - 3 a - 4\) , \( 1\) , \( -5 a^{2} + 10 a + 21\) , \( -a^{2} + 11\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(-5a^{2}+10a+21\right){x}-a^{2}+11$ |
| 6.1-b1 |
6.1-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{14} \cdot 3^{2} \) |
$3.38138$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.63228784$ |
1.162477121 |
\( -\frac{4196347}{288} a^{2} - \frac{16250291}{288} a - \frac{3290287}{144} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -30 a^{2} + 87 a + 54\) , \( 180 a^{2} - 518 a - 285\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-30a^{2}+87a+54\right){x}+180a^{2}-518a-285$ |
| 6.1-b2 |
6.1-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{7} \cdot 3^{4} \) |
$3.38138$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$32.63228784$ |
1.162477121 |
\( \frac{4674618922777}{648} a^{2} + \frac{2639892313973}{162} a + \frac{3969961625285}{648} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -470 a^{2} + 1347 a + 754\) , \( 10844 a^{2} - 31226 a - 17337\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-470a^{2}+1347a+754\right){x}+10844a^{2}-31226a-17337$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$3.61778$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.37836108$ |
1.972772430 |
\( -\frac{41609098317841}{6561} a^{2} + \frac{61434863448004}{6561} a + \frac{261995334002740}{6561} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 19\) , \( 6 a^{2} - 24 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(a^{2}-19\right){x}+6a^{2}-24a+3$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.61778$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$110.7567221$ |
1.972772430 |
\( \frac{9892984}{81} a^{2} - \frac{24588142}{81} a - \frac{28843189}{81} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 2 a - 4\) , \( -4 a^{2} + 10 a + 11\) , \( 7 a^{2} - 20 a - 12\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-4a^{2}+10a+11\right){x}+7a^{2}-20a-12$ |
| 9.2-b1 |
9.2-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$3.61778$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$31.08614384$ |
1.107398022 |
\( -\frac{41609098317841}{6561} a^{2} + \frac{61434863448004}{6561} a + \frac{261995334002740}{6561} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 2161 a^{2} - 3193 a - 13600\) , \( 88890 a^{2} - 131244 a - 559697\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(2161a^{2}-3193a-13600\right){x}+88890a^{2}-131244a-559697$ |
| 9.2-b2 |
9.2-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.61778$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$62.17228768$ |
1.107398022 |
\( \frac{9892984}{81} a^{2} - \frac{24588142}{81} a - \frac{28843189}{81} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 136 a^{2} - 203 a - 850\) , \( 1365 a^{2} - 2017 a - 8594\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(136a^{2}-203a-850\right){x}+1365a^{2}-2017a-8594$ |
| 10.1-a1 |
10.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{12} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$8.335044398$ |
1.781541974 |
\( \frac{38489481939691315982181}{3906250000} a^{2} + \frac{18119737965546747922113}{781250000} a + \frac{34428566326218836540273}{3906250000} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 4\) , \( 472 a^{2} - 709 a - 2987\) , \( 8705 a^{2} - 12802 a - 54737\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(472a^{2}-709a-2987\right){x}+8705a^{2}-12802a-54737$ |
| 10.1-a2 |
10.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$25.00513319$ |
1.781541974 |
\( -\frac{12417115772465721}{2500} a^{2} + \frac{1833327593795421}{250} a + \frac{78184883758192157}{2500} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 4\) , \( 472 a^{2} - 699 a - 2962\) , \( 8852 a^{2} - 13073 a - 55730\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(472a^{2}-699a-2962\right){x}+8852a^{2}-13073a-55730$ |
| 10.1-a3 |
10.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$50.01026639$ |
1.781541974 |
\( \frac{192688871}{200} a^{2} - \frac{56983307}{40} a - \frac{151482829}{25} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 4\) , \( 32 a^{2} - 49 a - 192\) , \( 130 a^{2} - 195 a - 814\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(32a^{2}-49a-192\right){x}+130a^{2}-195a-814$ |
| 10.1-a4 |
10.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{24} \cdot 5^{6} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$16.67008879$ |
1.781541974 |
\( -\frac{2601533072187}{4000000} a^{2} - \frac{718718821163}{400000} a - \frac{1416883072823}{2000000} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 4\) , \( -8 a^{2} + 11 a + 53\) , \( 481 a^{2} - 706 a - 3041\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(-8a^{2}+11a+53\right){x}+481a^{2}-706a-3041$ |
| 10.1-b1 |
10.1-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{12} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$3.758015870$ |
$2.609322967$ |
1.047959726 |
\( \frac{38489481939691315982181}{3906250000} a^{2} + \frac{18119737965546747922113}{781250000} a + \frac{34428566326218836540273}{3906250000} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -180 a^{2} - 398 a - 153\) , \( -4376 a^{2} - 9984 a - 3755\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-180a^{2}-398a-153\right){x}-4376a^{2}-9984a-3755$ |
| 10.1-b2 |
10.1-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5^{4} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1.252671956$ |
$70.45172012$ |
1.047959726 |
\( -\frac{12417115772465721}{2500} a^{2} + \frac{1833327593795421}{250} a + \frac{78184883758192157}{2500} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -8 a - 8\) , \( -8 a^{2} - 26 a - 2\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-8a-8\right){x}-8a^{2}-26a-2$ |
| 10.1-b3 |
10.1-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{2} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.626335978$ |
$140.9034402$ |
1.047959726 |
\( \frac{192688871}{200} a^{2} - \frac{56983307}{40} a - \frac{151482829}{25} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( 2 a + 2\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(2a+2\right){x}$ |
| 10.1-b4 |
10.1-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{24} \cdot 5^{6} \) |
$3.68187$ |
$(a+1), (a^2-2a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.879007935$ |
$5.218645935$ |
1.047959726 |
\( -\frac{2601533072187}{4000000} a^{2} - \frac{718718821163}{400000} a - \frac{1416883072823}{2000000} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( 0\) , \( -20 a^{2} + 2 a + 7\) , \( -120 a^{2} - 80 a - 11\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-20a^{2}+2a+7\right){x}-120a^{2}-80a-11$ |
| 12.1-a1 |
12.1-a |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$3.79547$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$124.6470861$ |
1.665138220 |
\( \frac{66272}{9} a^{2} - \frac{192224}{9} a - \frac{82496}{9} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -1\) , \( a^{2} - 2 a - 3\) , \( 3 a^{2} - 4 a - 23\) , \( 3 a^{2} - 4 a - 21\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}-{x}^{2}+\left(3a^{2}-4a-23\right){x}+3a^{2}-4a-21$ |
| 12.1-a2 |
12.1-a |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.79547$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$249.2941722$ |
1.665138220 |
\( -\frac{19904}{3} a^{2} + \frac{28928}{3} a + \frac{131264}{3} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -1\) , \( a + 1\) , \( 4322 a^{2} - 6383 a - 27211\) , \( -247658 a^{2} + 365654 a + 1559388\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4322a^{2}-6383a-27211\right){x}-247658a^{2}+365654a+1559388$ |
| 12.1-a3 |
12.1-a |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.79547$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$62.32354307$ |
1.665138220 |
\( \frac{1290068012}{3} a^{2} - \frac{3711983672}{3} a - \frac{2061432836}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 4\) , \( -145 a^{2} + 213 a + 914\) , \( 1062 a^{2} - 1568 a - 6688\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-145a^{2}+213a+914\right){x}+1062a^{2}-1568a-6688$ |
| 12.1-a4 |
12.1-a |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$3.79547$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$31.16177153$ |
1.665138220 |
\( -\frac{45411172}{81} a^{2} + \frac{85278952}{81} a + \frac{320161276}{81} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 2 a - 3\) , \( 658 a^{2} - 972 a - 4139\) , \( 15671 a^{2} - 23136 a - 98676\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(658a^{2}-972a-4139\right){x}+15671a^{2}-23136a-98676$ |
| 12.1-b1 |
12.1-b |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.79547$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.174111202$ |
$165.6836705$ |
2.312202309 |
\( -\frac{19904}{3} a^{2} + \frac{28928}{3} a + \frac{131264}{3} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 5\) , \( a^{2} - a - 4\) , \( 11 a^{2} - 19 a - 63\) , \( 18 a^{2} - 29 a - 109\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(11a^{2}-19a-63\right){x}+18a^{2}-29a-109$ |
| 12.1-b2 |
12.1-b |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$3.79547$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.348222404$ |
$165.6836705$ |
2.312202309 |
\( \frac{66272}{9} a^{2} - \frac{192224}{9} a - \frac{82496}{9} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 5\) , \( 0\) , \( -3 a^{2} - 16 a - 4\) , \( 8 a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-3a^{2}-16a-4\right){x}+8a^{2}+10a+2$ |
| 12.1-b3 |
12.1-b |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{4} \) |
$3.79547$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.174111202$ |
$165.6836705$ |
2.312202309 |
\( -\frac{45411172}{81} a^{2} + \frac{85278952}{81} a + \frac{320161276}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - a - 4\) , \( a^{2} - 4 a - 9\) , \( -a^{2} + a + 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(a^{2}-4a-9\right){x}-a^{2}+a+5$ |
| 12.1-b4 |
12.1-b |
$4$ |
$4$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3 \) |
$3.79547$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.696444808$ |
$41.42091762$ |
2.312202309 |
\( \frac{1290068012}{3} a^{2} - \frac{3711983672}{3} a - \frac{2061432836}{3} \) |
\( \bigl[a + 1\) , \( -a\) , \( a^{2} - 2 a - 3\) , \( -a^{2} + a + 3\) , \( -2 a^{2} + 5 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}+a+3\right){x}-2a^{2}+5a+3$ |
| 16.1-a1 |
16.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{15} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.911130699$ |
$15.74416286$ |
3.215645079 |
\( 1361807008595976 a^{2} - 3918468587454486 a - \frac{4352202913348235}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( -a + 1\) , \( a + 1\) , \( 4308 a^{2} - 6270 a - 27437\) , \( -131148 a^{2} + 194525 a + 822785\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4308a^{2}-6270a-27437\right){x}-131148a^{2}+194525a+822785$ |
| 16.1-a2 |
16.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.955565349$ |
$31.48832572$ |
3.215645079 |
\( 13631404 a^{2} - 39223118 a - \frac{87124519}{4} \) |
\( \bigl[a^{2} - a - 4\) , \( -a + 1\) , \( a + 1\) , \( -912 a^{2} + 1350 a + 5723\) , \( -16932 a^{2} + 25017 a + 106549\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-912a^{2}+1350a+5723\right){x}-16932a^{2}+25017a+106549$ |
| 16.1-a3 |
16.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{13} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.637043566$ |
$47.23248858$ |
3.215645079 |
\( \frac{905576451}{2} a^{2} + 1073151996 a + \frac{838075897}{2} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( 95 a^{2} - 128 a - 646\) , \( 974 a^{2} - 1377 a - 6341\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(95a^{2}-128a-646\right){x}+974a^{2}-1377a-6341$ |
| 16.1-a4 |
16.1-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{14} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.318521783$ |
$94.46497716$ |
3.215645079 |
\( -\frac{8025}{2} a^{2} - \frac{25027}{2} a - 7609 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( 5 a^{2} - 8 a - 36\) , \( 20 a^{2} - 29 a - 131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a^{2}-8a-36\right){x}+20a^{2}-29a-131$ |
| 16.1-b1 |
16.1-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$3.98188$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$126.5204058$ |
2.253551420 |
\( 15448391634 a^{2} + 36363567238 a + 13819003716 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( 21 a^{2} - 30 a - 127\) , \( -102 a^{2} + 152 a + 642\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(21a^{2}-30a-127\right){x}-102a^{2}+152a+642$ |
| 16.1-b2 |
16.1-b |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$3.98188$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$253.0408117$ |
2.253551420 |
\( -13556 a^{2} - 106016 a - 47580 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( a^{2} - 2\) , \( -3 a^{2} + 6 a + 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(a^{2}-2\right){x}-3a^{2}+6a+19$ |
| 16.1-c1 |
16.1-c |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{8} \) |
$3.98188$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$14.65446231$ |
0.261021802 |
\( 15448391634 a^{2} + 36363567238 a + 13819003716 \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 5\) , \( a + 1\) , \( -2 a^{2} - 2 a + 3\) , \( -20 a^{2} + 5 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-2a^{2}-2a+3\right){x}-20a^{2}+5a+8$ |
| 16.1-c2 |
16.1-c |
$2$ |
$2$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$3.98188$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$29.30892462$ |
0.261021802 |
\( -13556 a^{2} - 106016 a - 47580 \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 5\) , \( a + 1\) , \( -2 a^{2} + 8 a + 8\) , \( -a^{2} + 5 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-2a^{2}+8a+8\right){x}-a^{2}+5a+4$ |
| 16.1-d1 |
16.1-d |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.792833909$ |
$22.20057306$ |
1.881068226 |
\( 13631404 a^{2} - 39223118 a - \frac{87124519}{4} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3 a - 3\) , \( a^{2} - a - 4\) , \( -31 a^{2} + 86 a + 54\) , \( -251 a^{2} + 723 a + 395\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-31a^{2}+86a+54\right){x}-251a^{2}+723a+395$ |
| 16.1-d2 |
16.1-d |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{15} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.585667818$ |
$11.10028653$ |
1.881068226 |
\( 1361807008595976 a^{2} - 3918468587454486 a - \frac{4352202913348235}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3 a - 3\) , \( a^{2} - a - 4\) , \( -491 a^{2} + 1426 a + 734\) , \( -12855 a^{2} + 37015 a + 20451\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-491a^{2}+1426a+734\right){x}-12855a^{2}+37015a+20451$ |
| 16.1-d3 |
16.1-d |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{14} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.264277969$ |
$66.60171920$ |
1.881068226 |
\( -\frac{8025}{2} a^{2} - \frac{25027}{2} a - 7609 \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - 2 a - 3\) , \( -7 a^{2} + 21 a + 12\) , \( a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-7a^{2}+21a+12\right){x}+a^{2}-2a-2$ |
| 16.1-d4 |
16.1-d |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{13} \) |
$3.98188$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.528555939$ |
$33.30085960$ |
1.881068226 |
\( \frac{905576451}{2} a^{2} + 1073151996 a + \frac{838075897}{2} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - 2 a - 3\) , \( -77 a^{2} + 221 a + 122\) , \( -711 a^{2} + 2042 a + 1134\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-77a^{2}+221a+122\right){x}-711a^{2}+2042a+1134$ |
| 18.1-a1 |
18.1-a |
$2$ |
$7$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$2.650528859$ |
4.626637872 |
\( -\frac{4050945274021240859321348183991059}{2} a^{2} + \frac{8971539618999701814542549509635463}{3} a + \frac{25506944684150013566805332682224705}{2} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 4\) , \( a + 1\) , \( 77130715 a^{2} - 113652080 a - 486420485\) , \( -605961934787 a^{2} + 894771046541 a + 3815138047588\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(77130715a^{2}-113652080a-486420485\right){x}-605961934787a^{2}+894771046541a+3815138047588$ |
| 18.1-a2 |
18.1-a |
$2$ |
$7$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{14} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 7 \) |
$1$ |
$18.55370201$ |
4.626637872 |
\( -\frac{18864349985}{17496} a^{2} - \frac{21742231459}{8748} a - \frac{5049542471}{5832} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 3 a - 3\) , \( 1\) , \( -3 a^{2} + 10 a + 2\) , \( 82 a^{2} - 237 a - 128\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-3a^{2}+10a+2\right){x}+82a^{2}-237a-128$ |
| 18.1-b1 |
18.1-b |
$2$ |
$5$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.253614278$ |
$28.74642403$ |
3.895701559 |
\( -\frac{68647561059540444155}{162} a^{2} + \frac{152032247323353729097}{243} a + \frac{432242211188737821905}{162} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a\) , \( 1\) , \( 125752 a^{2} - 185700 a - 791688\) , \( -39647790 a^{2} + 58540978 a + 249634165\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(125752a^{2}-185700a-791688\right){x}-39647790a^{2}+58540978a+249634165$ |
| 18.1-b2 |
18.1-b |
$2$ |
$5$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{2} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.050722855$ |
$143.7321201$ |
3.895701559 |
\( -\frac{12247}{4} a^{2} + \frac{80207}{12} a + \frac{18717}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( 1\) , \( a^{2} - 2 a - 4\) , \( a - 1\) , \( -2 a^{2} - 4 a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+{x}^{2}+\left(a-1\right){x}-2a^{2}-4a-3$ |
| 18.1-c1 |
18.1-c |
$2$ |
$5$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{5} \cdot 3^{2} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$276.0224186$ |
1.966578306 |
\( -\frac{12247}{4} a^{2} + \frac{80207}{12} a + \frac{18717}{2} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 3 a^{2} - 3 a - 15\) , \( 2 a^{2} - 2 a - 11\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a^{2}-3a-15\right){x}+2a^{2}-2a-11$ |
| 18.1-c2 |
18.1-c |
$2$ |
$5$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{10} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.208179349$ |
1.966578306 |
\( -\frac{68647561059540444155}{162} a^{2} + \frac{152032247323353729097}{243} a + \frac{432242211188737821905}{162} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 5\) , \( 1\) , \( 56684793 a^{2} - 83692383 a - 356918127\) , \( 380460540780 a^{2} - 561731741337 a - 2395585551908\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(56684793a^{2}-83692383a-356918127\right){x}+380460540780a^{2}-561731741337a-2395585551908$ |
| 18.1-d1 |
18.1-d |
$2$ |
$7$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{7} \cdot 3^{14} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 7^{2} \) |
$0.370950946$ |
$55.93225255$ |
2.217363731 |
\( -\frac{18864349985}{17496} a^{2} - \frac{21742231459}{8748} a - \frac{5049542471}{5832} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - 2 a - 4\) , \( 386 a^{2} - 570 a - 2431\) , \( 6754 a^{2} - 9977 a - 42510\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}-a{x}^{2}+\left(386a^{2}-570a-2431\right){x}+6754a^{2}-9977a-42510$ |
| 18.1-d2 |
18.1-d |
$2$ |
$7$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{2} \) |
$4.06082$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 1 \) |
$2.596656626$ |
$0.163067791$ |
2.217363731 |
\( -\frac{4050945274021240859321348183991059}{2} a^{2} + \frac{8971539618999701814542549509635463}{3} a + \frac{25506944684150013566805332682224705}{2} \) |
\( \bigl[1\) , \( -a^{2} + a + 5\) , \( a\) , \( 34847754019 a^{2} - 51451007494 a - 219420427009\) , \( 5800201455994511 a^{2} - 8563719265927899 a - 36521208693335489\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(34847754019a^{2}-51451007494a-219420427009\right){x}+5800201455994511a^{2}-8563719265927899a-36521208693335489$ |
| 18.2-a1 |
18.2-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2 \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$14.94284268$ |
1.064633459 |
\( \frac{905576451}{2} a^{2} + 1073151996 a + \frac{838075897}{2} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 738 a^{2} - 1091 a - 4650\) , \( 18357 a^{2} - 27104 a - 115589\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(738a^{2}-1091a-4650\right){x}+18357a^{2}-27104a-115589$ |
| 18.2-a2 |
18.2-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$29.88568537$ |
1.064633459 |
\( -\frac{8025}{2} a^{2} - \frac{25027}{2} a - 7609 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 43 a^{2} - 66 a - 270\) , \( 349 a^{2} - 516 a - 2201\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(43a^{2}-66a-270\right){x}+349a^{2}-516a-2201$ |
| 18.2-a3 |
18.2-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$14.94284268$ |
1.064633459 |
\( 1361807008595976 a^{2} - 3918468587454486 a - \frac{4352202913348235}{2} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( 30680 a^{2} - 45290 a - 193203\) , \( -2563896 a^{2} + 3785500 a + 16143575\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(30680a^{2}-45290a-193203\right){x}-2563896a^{2}+3785500a+16143575$ |
| 18.2-a4 |
18.2-a |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$29.88568537$ |
1.064633459 |
\( 13631404 a^{2} - 39223118 a - \frac{87124519}{4} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 4\) , \( 0\) , \( -6360 a^{2} + 9390 a + 40047\) , \( -285232 a^{2} + 421132 a + 1795973\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-6360a^{2}+9390a+40047\right){x}-285232a^{2}+421132a+1795973$ |
| 18.2-b1 |
18.2-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{3} \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$15.59406267$ |
1.111030962 |
\( 1361807008595976 a^{2} - 3918468587454486 a - \frac{4352202913348235}{2} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - a - 4\) , \( a^{2} - a - 3\) , \( 24 a^{2} + 28 a - 360\) , \( -140 a^{2} + 732 a - 884\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(24a^{2}+28a-360\right){x}-140a^{2}+732a-884$ |
| 18.2-b2 |
18.2-b |
$4$ |
$6$ |
3.3.788.1 |
$3$ |
$[3, 0]$ |
18.2 |
\( 2 \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$4.06082$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$31.18812534$ |
1.111030962 |
\( 13631404 a^{2} - 39223118 a - \frac{87124519}{4} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - a - 4\) , \( a^{2} - a - 3\) , \( -16 a^{2} + 28 a + 90\) , \( 28 a^{2} - 30 a - 218\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-16a^{2}+28a+90\right){x}+28a^{2}-30a-218$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
