Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
2.0.3.1 |
$x^{2} - x + 1$ |
$2$ |
[0,1] |
$-\,3$ |
$1$ |
$1.73205080757$ |
$1.7320508075688772$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$6$ |
0 |
$1$ |
2.0.4.1 |
$x^{2} + 1$ |
$2$ |
[0,1] |
$-\,2^{2}$ |
$1$ |
$2.0$ |
$2.0$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$4$ |
0 |
$1$ |
2.2.5.1 |
$x^{2} - x - 1$ |
$2$ |
[2,0] |
$5$ |
$1$ |
$2.2360679775$ |
$2.23606797749979$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$0.48121182506$ |
2.0.7.1 |
$x^{2} - x + 2$ |
$2$ |
[0,1] |
$-\,7$ |
$1$ |
$2.64575131106$ |
$2.6457513110645907$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.0.8.1 |
$x^{2} + 2$ |
$2$ |
[0,1] |
$-\,2^{3}$ |
$1$ |
$2.82842712475$ |
$2.8284271247461903$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.2.8.1 |
$x^{2} - 2$ |
$2$ |
[2,0] |
$2^{3}$ |
$1$ |
$2.82842712475$ |
$2.8284271247461903$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$0.88137358702$ |
2.0.11.1 |
$x^{2} - x + 3$ |
$2$ |
[0,1] |
$-\,11$ |
$1$ |
$3.31662479036$ |
$3.3166247903554$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.2.12.1 |
$x^{2} - 3$ |
$2$ |
[2,0] |
$2^{2}\cdot 3$ |
$2$ |
$3.46410161514$ |
$3.4641016151377544$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.31695789692$ |
2.2.13.1 |
$x^{2} - x - 3$ |
$2$ |
[2,0] |
$13$ |
$1$ |
$3.60555127546$ |
$3.605551275463989$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.19476321729$ |
2.0.15.1 |
$x^{2} - x + 4$ |
$2$ |
[0,1] |
$-\,3\cdot 5$ |
$2$ |
$3.87298334621$ |
$3.872983346207417$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.17.1 |
$x^{2} - x - 4$ |
$2$ |
[2,0] |
$17$ |
$1$ |
$4.12310562562$ |
$4.123105625617661$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.09471254726$ |
2.0.19.1 |
$x^{2} - x + 5$ |
$2$ |
[0,1] |
$-\,19$ |
$1$ |
$4.35889894354$ |
$4.358898943540674$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.0.20.1 |
$x^{2} + 5$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 5$ |
$2$ |
$4.472135955$ |
$4.47213595499958$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.21.1 |
$x^{2} - x - 5$ |
$2$ |
[2,0] |
$3\cdot 7$ |
$2$ |
$4.58257569496$ |
$4.58257569495584$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.56679923697$ |
2.0.23.1 |
$x^{2} - x + 6$ |
$2$ |
[0,1] |
$-\,23$ |
$1$ |
$4.79583152331$ |
$4.795831523312719$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[3]$ |
$2$ |
0 |
$1$ |
2.0.24.1 |
$x^{2} + 6$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 3$ |
$2$ |
$4.89897948557$ |
$4.898979485566356$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.24.1 |
$x^{2} - 6$ |
$2$ |
[2,0] |
$2^{3}\cdot 3$ |
$2$ |
$4.89897948557$ |
$4.898979485566356$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.29243166956$ |
2.2.28.1 |
$x^{2} - 7$ |
$2$ |
[2,0] |
$2^{2}\cdot 7$ |
$2$ |
$5.29150262213$ |
$5.291502622129181$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.76865938331$ |
2.2.29.1 |
$x^{2} - x - 7$ |
$2$ |
[2,0] |
$29$ |
$1$ |
$5.38516480713$ |
$5.385164807134504$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.64723114637$ |
2.0.31.1 |
$x^{2} - x + 8$ |
$2$ |
[0,1] |
$-\,31$ |
$1$ |
$5.56776436283$ |
$5.5677643628300215$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[3]$ |
$2$ |
0 |
$1$ |
2.2.33.1 |
$x^{2} - x - 8$ |
$2$ |
[2,0] |
$3\cdot 11$ |
$2$ |
$5.74456264654$ |
$5.744562646538029$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$3.82816847133$ |
2.0.35.1 |
$x^{2} - x + 9$ |
$2$ |
[0,1] |
$-\,5\cdot 7$ |
$2$ |
$5.9160797831$ |
$5.916079783099616$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.37.1 |
$x^{2} - x - 9$ |
$2$ |
[2,0] |
$37$ |
$1$ |
$6.0827625303$ |
$6.082762530298219$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.49177985264$ |
2.0.39.1 |
$x^{2} - x + 10$ |
$2$ |
[0,1] |
$-\,3\cdot 13$ |
$2$ |
$6.2449979984$ |
$6.244997998398398$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.0.40.1 |
$x^{2} + 10$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 5$ |
$2$ |
$6.32455532034$ |
$6.324555320336759$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.40.1 |
$x^{2} - 10$ |
$2$ |
[2,0] |
$2^{3}\cdot 5$ |
$2$ |
$6.32455532034$ |
$6.324555320336759$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$1.81844645923$ |
2.2.41.1 |
$x^{2} - x - 10$ |
$2$ |
[2,0] |
$41$ |
$1$ |
$6.40312423743$ |
$6.4031242374328485$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$4.15912713463$ |
2.0.43.1 |
$x^{2} - x + 11$ |
$2$ |
[0,1] |
$-\,43$ |
$1$ |
$6.5574385243$ |
$6.557438524302$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.2.44.1 |
$x^{2} - 11$ |
$2$ |
[2,0] |
$2^{2}\cdot 11$ |
$2$ |
$6.63324958071$ |
$6.6332495807108$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.99322284613$ |
2.0.47.1 |
$x^{2} - x + 12$ |
$2$ |
[0,1] |
$-\,47$ |
$1$ |
$6.8556546004$ |
$6.855654600401044$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[5]$ |
$2$ |
0 |
$1$ |
2.0.51.1 |
$x^{2} - x + 13$ |
$2$ |
[0,1] |
$-\,3\cdot 17$ |
$2$ |
$7.14142842854$ |
$7.14142842854285$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.0.52.1 |
$x^{2} + 13$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 13$ |
$2$ |
$7.21110255093$ |
$7.211102550927978$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
0 |
$1$ |
2.2.53.1 |
$x^{2} - x - 13$ |
$2$ |
[2,0] |
$53$ |
$1$ |
$7.28010988928$ |
$7.280109889280518$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$1.96572047165$ |
2.0.55.1 |
$x^{2} - x + 14$ |
$2$ |
[0,1] |
$-\,5\cdot 11$ |
$2$ |
$7.4161984871$ |
$7.416198487095663$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.0.56.1 |
$x^{2} + 14$ |
$2$ |
[0,1] |
$-\,2^{3}\cdot 7$ |
$2$ |
$7.48331477355$ |
$7.483314773547883$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.2.56.1 |
$x^{2} - 14$ |
$2$ |
[2,0] |
$2^{3}\cdot 7$ |
$2$ |
$7.48331477355$ |
$7.483314773547883$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$3.40008441411$ |
2.2.57.1 |
$x^{2} - x - 14$ |
$2$ |
[2,0] |
$3\cdot 19$ |
$2$ |
$7.54983443527$ |
$7.54983443527075$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$5.71041605276$ |
2.0.59.1 |
$x^{2} - x + 15$ |
$2$ |
[0,1] |
$-\,59$ |
$1$ |
$7.68114574787$ |
$7.681145747868608$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[3]$ |
$2$ |
0 |
$1$ |
2.2.60.1 |
$x^{2} - 15$ |
$2$ |
[2,0] |
$2^{2}\cdot 3\cdot 5$ |
$3$ |
$7.74596669241$ |
$7.745966692414834$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$2.0634370689$ |
2.2.61.1 |
$x^{2} - x - 15$ |
$2$ |
[2,0] |
$61$ |
$1$ |
$7.81024967591$ |
$7.810249675906654$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$3.66421846089$ |
2.2.65.1 |
$x^{2} - x - 16$ |
$2$ |
[2,0] |
$5\cdot 13$ |
$2$ |
$8.0622577483$ |
$8.06225774829855$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
$[2]$ |
$2$ |
$1$ |
$2.77647228072$ |
2.0.67.1 |
$x^{2} - x + 17$ |
$2$ |
[0,1] |
$-\,67$ |
$1$ |
$8.18535277187$ |
$8.18535277187245$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
0 |
$1$ |
2.0.68.1 |
$x^{2} + 17$ |
$2$ |
[0,1] |
$-\,2^{2}\cdot 17$ |
$2$ |
$8.24621125124$ |
$8.246211251235321$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[4]$ |
$2$ |
0 |
$1$ |
2.2.69.1 |
$x^{2} - x - 17$ |
$2$ |
[2,0] |
$3\cdot 23$ |
$2$ |
$8.30662386292$ |
$8.306623862918075$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$3.21727197116$ |
2.0.71.1 |
$x^{2} - x + 18$ |
$2$ |
[0,1] |
$-\,71$ |
$1$ |
$8.42614977318$ |
$8.426149773176359$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[7]$ |
$2$ |
0 |
$1$ |
2.2.73.1 |
$x^{2} - x - 18$ |
$2$ |
[2,0] |
$73$ |
$1$ |
$8.54400374532$ |
$8.54400374531753$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$7.66669041926$ |
2.2.76.1 |
$x^{2} - 19$ |
$2$ |
[2,0] |
$2^{2}\cdot 19$ |
$2$ |
$8.71779788708$ |
$8.717797887081348$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$5.82893696698$ |
2.2.77.1 |
$x^{2} - x - 19$ |
$2$ |
[2,0] |
$7\cdot 11$ |
$2$ |
$8.77496438739$ |
$8.774964387392123$ |
|
✓ |
✓ |
$C_2$ (as 2T1) |
trivial |
$2$ |
$1$ |
$2.18464379161$ |
2.0.79.1 |
$x^{2} - x + 20$ |
$2$ |
[0,1] |
$-\,79$ |
$1$ |
$8.88819441732$ |
$8.888194417315589$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[5]$ |
$2$ |
0 |
$1$ |
2.0.83.1 |
$x^{2} - x + 21$ |
$2$ |
[0,1] |
$-\,83$ |
$1$ |
$9.11043357914$ |
$9.1104335791443$ |
✓ |
✓ |
✓ |
$C_2$ (as 2T1) |
$[3]$ |
$2$ |
0 |
$1$ |
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