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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. $p$

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Results (1-50 of 2102872 matches)

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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
6.0.273375.1	$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} + 3 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,3^{7}\cdot 5^{3}$	$2$	$8.0561300054$	$8.05613000539548$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$1.28284678343$
6.0.381391.1	$x^{6} - 2 x^{5} + x^{3} + 3 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,109\cdot 3499$	$2$	$8.51585791515$	$617.5686196691021$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$1.5100587354$
6.0.391127.1	$x^{6} - x^{5} - x^{4} + x^{3} + 5 x^{2} - 13 x + 9$	$6$	[0,3]	$-\,11\cdot 31^{2}\cdot 37$	$3$	$8.55171002381$	$112.32542009714453$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.63160569914$
6.0.392000.1	$x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 5^{3}\cdot 7^{2}$	$3$	$8.55488832192$	$16.364912636128995$			?	$S_3\times C_3$ (as 6T5)	$[2]$	$2$	$2$	$1.96225500494$
6.0.440896.1	$x^{6} - x^{4} - 3 x^{2} + 4$	$6$	[0,3]	$-\,2^{6}\cdot 83^{2}$	$2$	$8.72414134291$	$18.2208671582886$			?	$D_{6}$ (as 6T3)	$[2]$	$4$	$2$	$4.38387755257$
6.0.447471.1	$x^{6} - x^{5} - 5 x^{4} + 5 x^{3} + 14 x^{2} + 6 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 16573$	$2$	$8.74569140602$	$222.97757734803739$			✓	$C_3^2:D_4$ (as 6T13)	$[2]$	$6$	$2$	$4.80062553581$
6.0.451116.1	$x^{6} + 2 x^{4} - x^{3} + 4 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{2}\cdot 3^{3}\cdot 4177$	$3$	$8.7575247182$	$177.69676798542318$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.37334876479$
6.0.473416.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + 5 x^{2} + 3 x + 1$	$6$	[0,3]	$-\,2^{3}\cdot 17\cdot 59^{2}$	$3$	$8.82823371436$	$89.57678270623477$				$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$2.26379761163$
6.0.508707.1	$x^{6} - 2 x^{5} + x^{4} - 2 x^{3} + 5 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 83\cdot 227$	$3$	$8.93465839112$	$237.74566242099982$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$1.67000611362$
6.0.513932.1	$x^{6} - x^{5} + 2 x^{4} + x^{3} + 4 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,2^{2}\cdot 128483$	$2$	$8.94988819468$	$568.9963730176897$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.5737893854$
6.0.532703.1	$x^{6} - 2 x^{4} - 6 x^{3} - 3 x^{2} + 18 x + 17$	$6$	[0,3]	$-\,19\cdot 23^{2}\cdot 53$	$3$	$9.00355849415$	$152.1873844968761$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.50441527812$
6.0.560263.1	$x^{6} + 2 x^{4} - 2 x^{3} + 5 x^{2} - 14 x + 9$	$6$	[0,3]	$-\,11\cdot 31^{2}\cdot 53$	$3$	$9.0795708888$	$134.43585831168707$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.92968707723$
6.0.596375.1	$x^{6} - x^{5} - x^{3} + 3 x^{2} + x + 1$	$6$	[0,3]	$-\,5^{3}\cdot 13\cdot 367$	$3$	$9.1745880199$	$154.45063936416707$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.7623388034$
6.0.597248.1	$x^{6} + 3 x^{4} - 2 x^{3} + 5 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,2^{8}\cdot 2333$	$2$	$9.1768250169$	$121.7112427714352$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.68469453941$
6.0.599103.1	$x^{6} - 3 x^{5} - x^{4} + x^{3} + 10 x^{2} + 4 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 22189$	$2$	$9.18156928341$	$258.005813887982$			?	$C_3^2:D_4$ (as 6T13)	$[2]$	$6$	$2$	$5.52796293754$
6.0.603500.1	$x^{6} - x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} + 1$	$6$	[0,3]	$-\,2^{2}\cdot 5^{3}\cdot 17\cdot 71$	$4$	$9.19276614873$	$123.31766731588431$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.71398597286$
6.0.607000.1	$x^{6} - x^{5} + x^{4} + 3 x^{2} - 4 x + 4$	$6$	[0,3]	$-\,2^{3}\cdot 5^{3}\cdot 607$	$3$	$9.20163033186$	$155.82040944625965$			?	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$3.53869612312$
6.0.613111.1	$x^{6} - 2 x^{5} + 7 x^{4} - 2 x^{3} + 12 x^{2} + 10 x + 11$	$6$	[0,3]	$-\,19\cdot 23^{2}\cdot 61$	$3$	$9.21700559953$	$163.26971550168145$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.7015211795$
6.0.617584.1	$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} - 4 x^{2} + 4 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}\cdot 29$	$3$	$9.22817891536$	$28.351889352086026$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$3.52293402363$
6.0.641144.1	$x^{6} - x^{5} + x^{4} + 2 x^{3} + 5 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{3}\cdot 7\cdot 107^{2}$	$3$	$9.28594122301$	$77.40800992145451$				$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$2.69600129552$
6.0.643264.1	$x^{6} + 5 x^{4} + 15 x^{2} + 19$	$6$	[0,3]	$-\,2^{6}\cdot 19\cdot 23^{2}$	$3$	$9.29105165257$	$59.12698199637793$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.5632903894$
6.0.644463.1	$x^{6} + x^{4} - x^{3} + 4 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 23869$	$2$	$9.2939357274$	$267.5948429996363$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.4394807088$
6.0.644851.1	$x^{6} - x^{5} + 2 x^{4} - 8 x^{3} + 9 x^{2} - 3 x + 25$	$6$	[0,3]	$-\,23^{3}\cdot 53$	$2$	$9.29486806507$	$34.91418050019218$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.5558090755$
6.0.648000.1	$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 7 x^{2} - 4 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 3^{4}\cdot 5^{3}$	$3$	$9.30241765448$	$19.349808478363364$			✓	$S_3\times C_3$ (as 6T5)	$[2]$	$2$	$2$	$1.72572602223$
6.0.658503.1	$x^{6} - 2 x^{5} + 4 x^{4} - 9 x^{3} + 30 x^{2} - 9 x + 9$	$6$	[0,3]	$-\,3^{3}\cdot 29^{3}$	$2$	$9.32737905309$	$9.327379053088816$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.62180465573$
6.0.658503.2	$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + x^{2} + x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 29^{3}$	$2$	$9.32737905309$	$21.645076535339435$			✓	$S_4$ (as 6T8)	$[2]$	$2$	$2$	$1.99694638495$
6.0.676544.1	$x^{6} - 2 x^{4} - x^{2} + 11$	$6$	[0,3]	$-\,2^{6}\cdot 11\cdot 31^{2}$	$3$	$9.36949120349$	$52.230259428802384$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$2.2061399708$
6.0.677376.1	$x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 8 x^{2} - 4 x + 1$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 7^{2}$	$3$	$9.3714106217$	$17.926863604818365$			✓	$S_3\times C_3$ (as 6T5)	$[2]$	$2$	$2$	$1.82916788897$
6.0.686000.1	$x^{6} - 3 x^{5} + 8 x^{4} - 11 x^{3} + 8 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 5^{3}\cdot 7^{3}$	$3$	$9.39119127122$	$9.391191271220128$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.17170587094$
6.0.699840.1	$x^{6} + 3 x^{4} - 2 x^{3} + 3 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 3^{7}\cdot 5$	$3$	$9.42250681485$	$18.08540037460562$			✓	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$2.91332165652$
6.0.706023.1	$x^{6} - x^{5} + 7 x^{4} - 7 x^{3} + 14 x^{2} - 12 x + 7$	$6$	[0,3]	$-\,3^{3}\cdot 79\cdot 331$	$3$	$9.4363304617$	$280.083915996617$			?	$C_3^2:D_4$ (as 6T13)	$[2]$	$6$	$2$	$6.58006829962$
6.0.711232.1	$x^{6} - 2 x^{4} + 10 x^{2} - 6 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 11113$	$2$	$9.44789840805$	$210.83642948978243$			?	$C_3^2:D_4$ (as 6T13)	$[2]$	$4$	$2$	$5.72515749854$
6.0.711511.1	$x^{6} - 2 x^{5} + 3 x^{4} - 5 x^{3} + 3 x^{2} + 1$	$6$	[0,3]	$-\,181\cdot 3931$	$2$	$9.44851600609$	$843.5111143310443$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.17374214611$
6.0.719104.1	$x^{6} - 2 x^{5} + x^{4} + 4 x^{3} + x^{2} - 2 x + 1$	$6$	[0,3]	$-\,2^{8}\cdot 53^{2}$	$2$	$9.46524698233$	$20.591260281974$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$3.83484603648$
6.0.729399.1	$x^{6} - x^{5} - 3 x^{4} + 9 x^{3} - x^{2} - 21 x + 17$	$6$	[0,3]	$-\,3\cdot 11\cdot 23\cdot 31^{2}$	$4$	$9.48769818019$	$153.39165557487146$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.88462643451$
6.0.732024.1	$x^{6} - 2 x^{5} + 5 x^{4} - 9 x^{3} + 12 x^{2} - 10 x + 4$	$6$	[0,3]	$-\,2^{3}\cdot 3^{3}\cdot 3389$	$3$	$9.49338047107$	$285.19467035693356$			?	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$3.96606507147$
6.0.739071.1	$x^{6} - x^{5} + 7 x^{4} - 7 x^{3} + 17 x^{2} - 12 x + 16$	$6$	[0,3]	$-\,3^{3}\cdot 31\cdot 883$	$3$	$9.50855143896$	$286.5641289484781$			?	$C_3^2:D_4$ (as 6T13)	$[2]$	$6$	$2$	$5.90429622865$
6.0.742187.1	$x^{6} - 2 x^{5} + 10 x^{4} - 13 x^{3} + 30 x^{2} - 18 x + 27$	$6$	[0,3]	$-\,23^{3}\cdot 61$	$2$	$9.51522123817$	$37.456641600656084$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.63114265003$
6.0.756999.1	$x^{6} - 2 x^{5} + 10 x^{4} - 16 x^{3} + 31 x^{2} - 30 x + 25$	$6$	[0,3]	$-\,3^{3}\cdot 23^{2}\cdot 53$	$3$	$9.5466108043$	$60.473134530963414$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.67288067672$
6.0.771471.1	$x^{6} - 4 x^{4} - 3 x^{3} + 7 x^{2} + 15 x + 9$	$6$	[0,3]	$-\,3^{3}\cdot 28573$	$2$	$9.57678933662$	$292.77807294946115$			?	$C_3^2:D_4$ (as 6T13)	$[2]$	$6$	$2$	$5.9407161143$
6.0.771683.1	$x^{6} - 2 x^{5} + x^{4} - 6 x^{3} + 11 x^{2} + 5 x + 17$	$6$	[0,3]	$-\,11\cdot 31^{2}\cdot 73$	$3$	$9.57722790288$	$157.77515647274763$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$2.28356913689$
6.0.773927.1	$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 11 x^{2} - 9 x + 25$	$6$	[0,3]	$-\,7\cdot 11\cdot 19\cdot 23^{2}$	$4$	$9.58186393994$	$183.43663756185677$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.76400421158$
6.0.778688.1	$x^{6} + 3 x^{4} + 8 x^{2} + 23$	$6$	[0,3]	$-\,2^{6}\cdot 23^{3}$	$2$	$9.59166304663$	$13.564659966250536$			?	$S_4$ (as 6T8)	$[2]$	$2$	$2$	$1.869536401$
6.0.783875.1	$x^{6} - x^{5} - 2 x^{4} + x^{3} + 5 x^{2} - 4 x + 1$	$6$	[0,3]	$-\,5^{3}\cdot 6271$	$2$	$9.60228228245$	$177.07343109568978$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.03736653284$
6.0.797375.1	$x^{6} - 3 x^{5} + 5 x^{4} - 3 x^{3} + 2 x^{2} + x + 1$	$6$	[0,3]	$-\,5^{3}\cdot 6379$	$2$	$9.62964852214$	$178.5917131336166$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.85526046764$
6.0.805111.1	$x^{6} - x^{5} - x^{4} - x^{3} + 4 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,805111$	$1$	$9.64515682407$	$897.2797779956929$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.03091889152$
6.0.817711.1	$x^{6} - 2 x^{4} - x^{3} + 3 x^{2} - x + 1$	$6$	[0,3]	$-\,817711$	$1$	$9.67015213549$	$904.2737417397456$			✓	$S_6$ (as 6T16)	$[2]$	$2$	$2$	$2.25034091314$
6.0.839056.1	$x^{6} + 6 x^{4} + 8 x^{2} + 1$	$6$	[0,3]	$-\,2^{4}\cdot 229^{2}$	$2$	$9.71177229422$	$42.80186911806539$	✓		?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$4.71090918169$
6.0.854335.1	$x^{6} - x^{5} + 5 x^{4} + 5 x^{3} + 9 x^{2} + 17 x + 23$	$6$	[0,3]	$-\,5\cdot 17\cdot 19\cdot 23^{2}$	$4$	$9.74102593834$	$192.73038162158036$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$1.70273116141$
6.0.861184.2	$x^{6} - 3 x^{4} + 5 x^{2} + 1$	$6$	[0,3]	$-\,2^{10}\cdot 29^{2}$	$2$	$9.75399792215$	$21.540659228538015$			?	$S_4\times C_2$ (as 6T11)	$[2]$	$2$	$2$	$4.15385489663$

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Elliptic curves over $\Q$
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