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Results (1-50 of 87 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
11.1.41943325311670611.1	$x^{11} + 4 x - 1$	$11$	[1,5]	$-\,3\cdot 2963\cdot 31513\cdot 149733923$	$4$	$32.4452532955$	$204800696.56051126$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$7816.22208317$
11.1.74046177941851136.1	$x^{11} + 6 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 7\cdot 177379\cdot 58237463$	$4$	$34.1657650225$	$15968531.424557826$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$15207.589824$
11.1.725...000.1	$x^{11} + 90 x^{7} - 96 x^{6} + 720 x^{4} - 855 x^{3} + 1728 x - 2160$	$11$	[1,5]	$-\,2^{22}\cdot 3^{11}\cdot 5^{10}$	$3$	$51.8332598222$	$330.33204764416007$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$810226.020134$
11.1.206...096.1	$x^{11} + 9 x - 6$	$11$	[1,5]	$-\,2^{8}\cdot 3^{10}\cdot 539621\cdot 2536579$	$4$	$57.0139179175$	$10683602.108974101$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$328177.989535$
11.1.241...000.1	$x^{11} - 2 x^{10} - 14 x^{9} + 32 x^{8} + 56 x^{7} - 160 x^{6} - 28 x^{5} + 152 x^{4} + 74 x^{3} - 68 x^{2} - 44 x - 8$	$11$	[1,5]	$-\,2^{23}\cdot 3^{10}\cdot 5^{11}$	$3$	$57.8286367131$	$316.6977294123614$		$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$1040140.37741$
11.1.858...611.1	$x^{11} + 8 x - 1$	$11$	[1,5]	$-\,187699\cdot 16589257\cdot 27586777$	$3$	$64.8904664828$	$9268190017.7603$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$389784.406006$
11.1.858...664.1	$x^{11} + 8 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 84261157\cdot 995552023$	$3$	$64.8904865272$	$543887804.8721827$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$235453.462516$
11.1.146...000.1	$x^{11} - x^{10} - 5 x^{9} - 35 x^{8} + 80 x^{7} + 112 x^{6} + 288 x^{5} - 1440 x^{4} + 1728 x - 1728$	$11$	[1,5]	$-\,2^{20}\cdot 3^{15}\cdot 5^{10}$	$3$	$68.1356548569$	$316.5737466750152$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2378945.80742$
11.1.232...000.1	$x^{11} - 5 x^{8} + 12 x^{6} + 40 x^{5} + 45 x^{3} + 36 x + 15$	$11$	[1,5]	$-\,2^{27}\cdot 3^{11}\cdot 5^{10}$	$3$	$71.0297586385$	$433.58553218631477$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2543201.52918$
11.1.286...464.1	$x^{11} - 7 x - 8$	$11$	[1,5]	$-\,2^{10}\cdot 857\cdot 326559088504073$	$3$	$72.4017932693$	$1058038068.9710376$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$892974.551877$
11.1.306...464.1	$x^{11} + x - 8$	$11$	[1,5]	$-\,2^{10}\cdot 3\cdot 2237\cdot 44579193910351$	$4$	$72.8422886301$	$1093930473.7182624$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2113619.24959$
11.1.313...611.1	$x^{11} + 9 x - 1$	$11$	[1,5]	$-\,23384419\cdot 13419644780369$	$2$	$73.0017747771$	$17714700008.052963$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$691054.996495$
11.3.605...000.1	$x^{11} - 4 x^{10} + 320 x^{6} - 1680 x^{5} + 3900 x^{4} - 5075 x^{3} + 3900 x^{2} - 1680 x + 320$	$11$	[3,4]	$2^{18}\cdot 5^{19}\cdot 11^{2}$	$3$	$77.4908614005$	$438.00921833709043$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$6$	$2781030.35764$
11.1.620...464.1	$x^{11} + 9 x - 8$	$11$	[1,5]	$-\,2^{10}\cdot 32261\cdot 18772717230301$	$3$	$77.6654244452$	$1556440336.8799467$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$1936880.52265$
11.1.908...011.1	$x^{11} - 8 x - 9$	$11$	[1,5]	$-\,7\cdot 13\cdot 29\cdot 5653\cdot 60926710628633$	$5$	$80.4119428291$	$30148315650.95611$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2243649.51846$
11.1.994...011.1	$x^{11} - 4 x - 9$	$11$	[1,5]	$-\,97\cdot 101293\cdot 547747\cdot 184839653$	$4$	$81.0744872959$	$31540106839.858437$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2029175.80135$
11.1.994...011.1	$x^{11} - x - 9$	$11$	[1,5]	$-\,7\cdot 433\cdot 121063\cdot 2711110774787$	$4$	$81.0747980498$	$31540771748.63806$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2267127.71033$
11.1.994...011.1	$x^{11} + 4 x - 9$	$11$	[1,5]	$-\,157\cdot 199\cdot 12708721\cdot 2505580537$	$4$	$81.0751087921$	$31541436643.718132$	✓	$S_{11}$ (as 11T8)	$[2, 2]$	$2$	$5$	$1125628.91301$
11.1.995...011.1	$x^{11} + 5 x - 9$	$11$	[1,5]	$-\,13\cdot 277\cdot 64037\cdot 4316220682903$	$4$	$81.0784148269$	$31548511276.440365$	✓	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2428526.81491$
11.1.161...000.1	$x^{11} - x^{10} - 9 x^{9} + 9 x^{8} - 24 x^{7} + 56 x^{6} + 224 x^{5} - 384 x^{4} + 384 x^{3} - 1024 x^{2} + 1080 x + 200$	$11$	[1,5]	$-\,2^{21}\cdot 5^{8}\cdot 7^{11}$	$3$	$84.7487867121$	$649.2668607063579$		$S_{11}$ (as 11T8)	$[3]$	$2$	$5$	$8618230.56599$
11.3.467...088.1	$x^{11} - 33 x^{8} + 6912$	$11$	[3,4]	$2^{25}\cdot 3^{10}\cdot 11^{9}$	$3$	$93.3155965637$	$375.2910237322625$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$6$	$14201368.0947$
11.1.222...000.1	$x^{11} - x^{10} - 5 x^{9} - 35 x^{8} + 80 x^{7} + 112 x^{6} + 288 x^{5} - 1440 x^{4} + 2304 x - 2304$	$11$	[1,5]	$-\,2^{32}\cdot 3^{12}\cdot 5^{10}$	$3$	$107.559014568$	$822.3326065593775$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$31672884.2134$
11.1.290...000.1	$x^{11} + 90 x^{7} - 64 x^{6} + 1080 x^{4} - 855 x^{3} + 3888 x - 3240$	$11$	[1,5]	$-\,2^{27}\cdot 3^{11}\cdot 5^{13}$	$3$	$110.171312145$	$2046.0745529845115$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$57156027.1985$
11.1.348...000.1	$x^{11} - x^{10} - 29 x^{9} + 37 x^{8} + 305 x^{7} - 521 x^{6} - 1237 x^{5} + 3325 x^{4} - 85 x^{3} - 7875 x^{2} + 11025 x - 5145$	$11$	[1,5]	$-\,2^{18}\cdot 3^{10}\cdot 5^{8}\cdot 7^{8}$	$4$	$112.021068616$	$1308.0671988554775$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$50176456.8689$
11.3.364...081.1	$x^{11} + 20 x^{9} - 26 x^{8} + 72 x^{7} - 137 x^{6} + 199 x^{5} - 212 x^{4} + 98 x^{3} - 11 x^{2} + x - 1$	$11$	[3,4]	$661^{8}$	$1$	$112.474897717$	$180.36869686739456$	?	$M_{11}$ (as 11T6)	$[2]$	$2$	$6$	$6961764.90605$
11.1.188...216.1	$x^{11} - 22 x^{7} + 121 x^{3} - 192$	$11$	[1,5]	$-\,2^{25}\cdot 3^{9}\cdot 11^{11}$	$3$	$130.594143642$	$1440.1372617849388$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$56729837.6159$
11.1.360...000.1	$x^{11} - 3 x^{10} - 25 x^{9} + 195 x^{8} + 270 x^{7} - 3642 x^{6} + 4226 x^{5} + 39450 x^{4} - 55695 x^{3} - 169795 x^{2} + 510231 x + 985507$	$11$	[1,5]	$-\,2^{15}\cdot 5^{19}\cdot 7^{8}$	$3$	$170.774896453$	$1467.8269822132863$		$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$1216049840.91$
11.1.757...064.3	$x^{11} - 22$	$11$	[1,5]	$-\,2^{10}\cdot 11^{21}$	$2$	$182.716152011$	$222.3216702379646$	✓	$F_{11}$ (as 11T4)	$[2]$	$2$	$5$	$220610692.318$
11.1.108...000.1	$x^{11} - 25 x^{8} + 300 x^{6} + 1000 x^{5} + 5625 x^{3} + 22500 x + 9375$	$11$	[1,5]	$-\,2^{27}\cdot 3^{12}\cdot 5^{16}$	$3$	$188.830161445$	$2135.278125289271$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$779700313.751$
11.1.162...655.1	$x^{11} + 11 x^{9} - 216513$	$11$	[1,5]	$-\,3^{12}\cdot 5\cdot 11^{19}$	$3$	$241.43922332$	$1135.4496198838813$		$S_{11}$ (as 11T8)	$[3]$	$2$	$5$	$678643197.709$
11.1.172...216.1	$x^{11} - 55 x^{9} - 154 x^{8} - 1760 x^{7} - 11616 x^{6} - 3124 x^{5} - 51656 x^{4} - 267476 x^{3} - 202928 x^{2} + 282876 x - 985560$	$11$	[1,5]	$-\,2^{21}\cdot 3^{9}\cdot 11^{15}$	$3$	$242.742878765$	$1758.8518210797943$		$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$15786766973.5$
11.1.185...864.1	$x^{11} - 11616 x^{2} + 38016 x - 31104$	$11$	[1,5]	$-\,2^{8}\cdot 3^{26}\cdot 11^{11}$	$3$	$244.379481268$	$740.8348733198401$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$1040851970.6$
11.1.434...664.1	$x^{11} - 22 x^{8} - 12288$	$11$	[1,5]	$-\,2^{33}\cdot 3^{11}\cdot 11^{11}$	$3$	$264.0$	$1703.9966148005913$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2658557996.18$
11.1.148...912.1	$x^{11} - 11 x^{9} - 118098$	$11$	[1,5]	$-\,2^{11}\cdot 3^{26}\cdot 11^{11}$	$3$	$295.232271748$	$1308.551054254072$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$2702046238.44$
11.1.148...912.2	$x^{11} - 144342 x^{2} - 2125764$	$11$	[1,5]	$-\,2^{11}\cdot 3^{26}\cdot 11^{11}$	$3$	$295.232271748$	$1308.551054254072$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$5844819686.5$
11.3.170...696.4	$x^{11} - 132 x^{9} - 638 x^{8} + 7260 x^{7} + 43560 x^{6} - 18876 x^{5} - 1019304 x^{4} - 3972672 x^{3} - 6496248 x^{2} - 2230272 x + 5287392$	$11$	[3,4]	$2^{6}\cdot 3^{14}\cdot 11^{18}$	$3$	$298.910061494$	$496.8248577356094$		$\PSL(2,11)$ (as 11T5)	$[3]$	$2$	$6$	$26101040567.7$
11.1.246...144.1	$x^{11} - 11 x^{9} - 484 x^{8} + 627 x^{7} + 13772 x^{6} + 21703 x^{5} - 366036 x^{4} - 76208 x^{3} + 4361588 x^{2} - 10159776 x + 11073344$	$11$	[1,5]	$-\,2^{11}\cdot 3^{9}\cdot 11^{19}$	$3$	$309.151326855$	$2575.8940569283013$		$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$11839309185.9$
11.1.445...000.1	$x^{11} + 880 x - 800$	$11$	[1,5]	$-\,2^{12}\cdot 5^{18}\cdot 11^{11}$	$3$	$326.255725628$	$1105.4950275609754$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$5998242116.93$
11.1.725...000.1	$x^{11} - 5 x^{10} - 5 x^{9} + 105 x^{8} - 390 x^{7} - 4322 x^{6} - 10650 x^{5} - 14670 x^{4} - 13805 x^{3} - 9535 x^{2} - 3799 x - 1245$	$11$	[1,5]	$-\,2^{31}\cdot 3^{11}\cdot 5^{19}$	$3$	$341.028237793$	$4379.952569208022$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$12115158466.9$
11.1.253...208.3	$x^{11} - 4312 x^{4} + 614656$	$11$	[1,5]	$-\,2^{17}\cdot 7^{14}\cdot 11^{11}$	$3$	$382.120365017$	$3724.2976664574426$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$13573685854.2$
11.1.253...208.5	$x^{11} - 44 x^{9} + 484 x^{7} - 702464$	$11$	[1,5]	$-\,2^{17}\cdot 7^{14}\cdot 11^{11}$	$3$	$382.120365017$	$3724.2976664574426$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$15782775502.1$
11.1.490...383.1	$x^{11} - 26411 x^{2} - 151263$	$11$	[1,5]	$-\,3^{18}\cdot 7^{9}\cdot 11^{12}$	$3$	$405.744339486$	$1199.6528218367284$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$15057228670.3$
11.3.251...928.1	$x^{11} + 66 x^{9} - 1881 x^{8} - 21780 x^{7} - 193644 x^{6} - 1085832 x^{5} + 749628 x^{4} + 5588352 x^{3} - 5436288 x^{2} - 1596672 x - 819072$	$11$	[3,4]	$2^{22}\cdot 3^{15}\cdot 11^{15}$	$3$	$470.718013684$	$2766.2945457924825$		$S_{11}$ (as 11T8)	$[2]$	$2$	$6$	$391564659981$
11.3.804...000.1	$x^{11} - 1002375 x - 2733750$	$11$	[3,4]	$2^{8}\cdot 3^{8}\cdot 5^{16}\cdot 11^{12}$	$4$	$523.210646029$	$2528.7846779194647$	?	$A_{11}$ (as 11T7)	$[2]$	$2$	$6$	$349151835202$
11.3.898...488.1	$x^{11} - 264 x^{9} - 374 x^{8} + 25872 x^{7} + 76296 x^{6} - 1052832 x^{5} - 5170176 x^{4} + 9415296 x^{3} + 112953984 x^{2} + 281521152 x + 245113344$	$11$	[3,4]	$2^{10}\cdot 3^{15}\cdot 11^{19}$	$3$	$528.509391066$	$2085.019329984618$		$S_{11}$ (as 11T8)	$[2]$	$2$	$6$	$860600137219$
11.1.209...539.3	$x^{11} - 3107227739$	$11$	[1,5]	$-\,7^{10}\cdot 11^{21}$	$2$	$570.668963394$	$694.3670589522617$	?	$F_{11}$ (as 11T4)	$[2]$	$2$	$5$	$69248281708.1$
11.1.209...539.9	$x^{11} - 847$	$11$	[1,5]	$-\,7^{10}\cdot 11^{21}$	$2$	$570.668963394$	$694.3670589522617$	?	$F_{11}$ (as 11T4)	$[2]$	$2$	$5$	$70243113861.9$
11.1.424...808.1	$x^{11} + 9801 x^{7} - 39204 x^{6} - 215622 x^{5} + 2352240 x^{4} + 4263435 x^{3} - 46574352 x^{2} + 38106288 x + 381928932$	$11$	[1,5]	$-\,2^{18}\cdot 3^{7}\cdot 11^{21}$	$3$	$608.597919003$	$1965.8298127772184$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$135515170939$
11.1.978...000.1	$x^{11} + 166375 x^{3} - 6655000$	$11$	[1,5]	$-\,2^{14}\cdot 5^{10}\cdot 11^{19}$	$3$	$656.637294722$	$2224.507141113468$		$S_{11}$ (as 11T8)	$[2, 2]$	$2$	$5$	$841957315670$
11.1.136...112.1	$x^{11} + 154 x^{7} - 537824$	$11$	[1,5]	$-\,2^{17}\cdot 7^{16}\cdot 11^{12}$	$3$	$676.902994448$	$6085.225858262105$	?	$S_{11}$ (as 11T8)	$[2]$	$2$	$5$	$255472708901$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.