LMFDB - Number field search results

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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

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Results (1-50 of 26310 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
7.1.10083695.1	$x^{7} - 2 x^{6} + 2 x^{5} - 3 x^{4} + 5 x^{3} - 7 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,5\cdot 2016739$	$2$	$10.0119137626$	$3175.4834277634013$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.06765004232$
7.1.10336279.1	$x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 4 x^{3} + x^{2} - 2 x - 1$	$7$	[1,3]	$-\,149\cdot 69371$	$2$	$10.0473615841$	$3215.0083981227795$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.5789953247$
7.1.11976527.1	$x^{7} - 3 x^{6} + 7 x^{5} - 13 x^{4} + 15 x^{3} - 11 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,1193\cdot 10039$	$2$	$10.2610104114$	$3460.71192097811$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.30925645965$
7.1.12959975.1	$x^{7} - 3 x^{6} + 4 x^{5} - 4 x^{4} + 4 x^{2} - 1$	$7$	[1,3]	$-\,5^{2}\cdot 7\cdot 103\cdot 719$	$4$	$10.3773462855$	$2105.2907409444106$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.81550479114$
7.1.13750883.1	$x^{7} - x^{6} + 3 x^{4} - 5 x^{3} + 2 x^{2} + 1$	$7$	[1,3]	$-\,1217\cdot 11299$	$2$	$10.4655368786$	$3708.2183053320905$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.6745917987$
7.1.13841499.1	$x^{7} + 5 x^{5} - 2 x^{4} + 7 x^{3} - 3 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,3\cdot 7\cdot 797\cdot 827$	$4$	$10.4753614699$	$3720.4165089409007$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.59642878355$
7.1.14060315.1	$x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - 4 x^{3} + 5 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,5\cdot 2812063$	$2$	$10.4988601338$	$3749.708655349106$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.40256700811$
7.1.14201651.1	$x^{7} - 2 x^{6} + x^{5} - x^{4} + 4 x^{3} - 5 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,14201651$	$1$	$10.5138721305$	$3768.5077948705375$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.48944889479$
7.1.14352952.1	$x^{7} - 2 x^{5} - 2 x^{4} + x^{3} + 5 x^{2} - 4$	$7$	[1,3]	$-\,2^{3}\cdot 41\cdot 43759$	$3$	$10.5298013012$	$3788.529002132622$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.53270784027$
7.1.14621967.1	$x^{7} - x^{6} - 2 x^{5} + 3 x^{4} + 2 x^{2} - 3 x + 1$	$7$	[1,3]	$-\,3^{2}\cdot 1624663$	$2$	$10.5577714672$	$2207.7112582944355$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.9662549373$
7.1.15293507.1	$x^{7} - x^{6} - x^{5} - 2 x^{4} + 6 x^{2} + 5 x + 1$	$7$	[1,3]	$-\,15293507$	$1$	$10.6257148035$	$3910.691371100512$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.18492675134$
7.1.15395703.1	$x^{7} + 2 x^{5} - 2 x^{4} - 3 x^{3} - 6 x^{2} - 1$	$7$	[1,3]	$-\,3\cdot 743\cdot 6907$	$3$	$10.6358293525$	$3923.7358473781082$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.24687920776$
7.1.15793499.1	$x^{7} - 2 x^{6} + x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$	$7$	[1,3]	$-\,15793499$	$1$	$10.6746599973$	$3974.103546713397$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.84396240567$
7.1.15972400.1	$x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} - 2 x - 1$	$7$	[1,3]	$-\,2^{4}\cdot 5^{2}\cdot 73\cdot 547$	$4$	$10.6918506227$	$927.5167470599285$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.08755705666$
7.1.15992471.1	$x^{7} - 3 x^{6} + 7 x^{5} - 11 x^{4} + 10 x^{3} - 4 x^{2} + 1$	$7$	[1,3]	$-\,11\cdot 19\cdot 76519$	$3$	$10.6937689376$	$3999.05876425941$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.67398462754$
7.1.16126423.1	$x^{7} - 2 x^{5} + 4 x^{3} - 4 x^{2} + x - 1$	$7$	[1,3]	$-\,3041\cdot 5303$	$2$	$10.7065190104$	$4015.7717813640757$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.04327111094$
7.1.16142827.1	$x^{7} - 2 x^{6} - x^{4} + 5 x^{3} - 2 x^{2} - x + 1$	$7$	[1,3]	$-\,16142827$	$1$	$10.708074162$	$4017.8137089715847$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.18937677367$
7.1.16368832.1	$x^{7} - 2 x^{6} + 3 x^{5} - x^{4} - x^{3} - 3 x^{2} - 1$	$7$	[1,3]	$-\,2^{6}\cdot 255763$	$2$	$10.7293634237$	$1430.4209170730132$		$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.80322901297$
7.1.16528892.1	$x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + 3 x + 1$	$7$	[1,3]	$-\,2^{2}\cdot 523\cdot 7901$	$3$	$10.7442888999$	$3226.848227159047$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.72869749329$
7.1.16645243.1	$x^{7} - 2 x^{6} + x^{5} - 3 x^{4} + 6 x^{3} - 4 x^{2} + 3 x - 1$	$7$	[1,3]	$-\,347\cdot 47969$	$2$	$10.7550609792$	$4079.8582083204806$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.69473239622$
7.1.16804051.1	$x^{7} - 2 x^{6} + 3 x^{5} - 6 x^{4} + 9 x^{3} - 9 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,11\cdot 47\cdot 32503$	$3$	$10.7696601474$	$4099.274447996865$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.65674648666$
7.1.16868779.1	$x^{7} - 2 x^{6} + 3 x^{5} + x^{4} - 6 x^{3} + 5 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,193\cdot 87403$	$2$	$10.7755766672$	$4107.161915483733$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.92713833489$
7.1.17030407.1	$x^{7} - x^{6} + 2 x^{5} + x^{4} - 3 x^{2} + 2 x - 1$	$7$	[1,3]	$-\,61\cdot 279187$	$2$	$10.7902658943$	$4126.791368605881$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.1956297015$
7.1.17179595.1	$x^{7} - 2 x^{6} + 5 x^{4} - 9 x^{3} + 8 x^{2} - 3 x + 1$	$7$	[1,3]	$-\,5\cdot 101\cdot 34019$	$3$	$10.8037188663$	$4144.827499426243$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$3.75725533522$
7.1.17186635.1	$x^{7} - x^{6} + 4 x^{5} - 6 x^{4} + 9 x^{3} - 11 x^{2} + 6 x - 1$	$7$	[1,3]	$-\,5\cdot 23\cdot 199\cdot 751$	$4$	$10.804351218$	$4145.676663706421$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.02215566071$
7.1.17241884.1	$x^{7} + 2 x^{5} - 4 x^{4} - 2 x^{3} - 5 x^{2} - x - 1$	$7$	[1,3]	$-\,2^{2}\cdot 11\cdot 391861$	$3$	$10.8093061383$	$3295.7102869825812$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.99473487965$
7.1.17258864.1	$x^{7} - 2 x^{5} - x^{4} + 3 x^{3} + 2 x + 1$	$7$	[1,3]	$-\,2^{4}\cdot 7\cdot 154097$	$3$	$10.810826229$	$1808.2984434251275$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.03467064725$
7.1.17721559.1	$x^{7} - x^{6} + x^{4} + 2 x^{3} - 5 x^{2} + 2 x + 1$	$7$	[1,3]	$-\,3323\cdot 5333$	$2$	$10.8517623676$	$4209.698207710382$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.37453994646$
7.1.17854963.1	$x^{7} - 3 x^{6} + 3 x^{5} - x^{4} + 8 x^{3} - 4 x^{2} - x + 1$	$7$	[1,3]	$-\,7^{2}\cdot 109\cdot 3343$	$3$	$10.8633948471$	$2208.9207283825685$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.71810612089$
7.1.18179396.1	$x^{7} - 4 x^{5} + 7 x^{3} - 3 x^{2} - 4 x + 4$	$7$	[1,3]	$-\,2^{2}\cdot 4544849$	$2$	$10.8913766829$	$4263.730291657764$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.61609287505$
7.1.18233127.1	$x^{7} - 2 x^{6} + 3 x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$	$7$	[1,3]	$-\,3^{3}\cdot 11^{2}\cdot 5581$	$3$	$10.895969517$	$892.6759156248582$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.41124451669$
7.1.18257047.1	$x^{7} - 2 x^{6} + x^{5} - 4 x^{4} + 7 x^{3} - 2 x^{2} - x + 1$	$7$	[1,3]	$-\,31\cdot 588937$	$2$	$10.8980104268$	$4272.826582018044$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.65354481949$
7.1.18290639.1	$x^{7} - x^{4} + 4 x^{3} - 2 x^{2} - 1$	$7$	[1,3]	$-\,18290639$	$1$	$10.900872708$	$4276.755662882789$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.86045039511$
7.1.18538123.1	$x^{7} - 3 x^{6} + 4 x^{5} - 3 x^{4} + 3 x^{3} - x^{2} - x - 1$	$7$	[1,3]	$-\,18538123$	$1$	$10.9218223572$	$4305.592061493982$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.02339637893$
7.1.18884027.2	$x^{7} - x^{5} - 2 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$	$7$	[1,3]	$-\,229\cdot 82463$	$2$	$10.9507051974$	$4345.575566021145$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.3267643622$
7.1.19083235.1	$x^{7} - 3 x^{6} + 2 x^{5} + 3 x^{4} - 3 x^{3} - 4 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,5\cdot 3816647$	$2$	$10.9671338177$	$4368.436219060546$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.83362875421$
7.1.19202359.1	$x^{7} - x^{6} - 3 x^{5} + x^{4} + 8 x^{3} + 5 x^{2} - x - 1$	$7$	[1,3]	$-\,11\cdot 1745669$	$2$	$10.976887833$	$4382.049634588819$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.53268257407$
7.1.19252547.1	$x^{7} - x^{4} + 2 x^{3} + x^{2} + 2 x - 1$	$7$	[1,3]	$-\,2129\cdot 9043$	$2$	$10.9809817642$	$4387.772441683821$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$7.46788510372$
7.1.19275243.1	$x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} - 2 x + 1$	$7$	[1,3]	$-\,3\cdot 13\cdot 494237$	$3$	$10.9828301174$	$4390.3579580713$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.68203170321$
7.1.19543760.1	$x^{7} - 2 x^{6} + x^{5} - 3 x^{4} + 3 x^{3} - x^{2} - 2 x - 1$	$7$	[1,3]	$-\,2^{4}\cdot 5\cdot 244297$	$3$	$11.0045576189$	$3126.0006397952$		$S_7$ (as 7T7)	$[2]$	$2$	$3$	$7.42307777335$
7.1.19810672.1	$x^{7} + 2 x^{5} - x^{4} - 3 x^{3} - 2 x^{2} - 1$	$7$	[1,3]	$-\,2^{4}\cdot 7\cdot 79\cdot 2239$	$4$	$11.0259031279$	$1937.3746328505904$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.39164045847$
7.1.19844884.1	$x^{7} - x^{6} + 2 x^{4} + 4 x^{2} + 9 x + 1$	$7$	[1,3]	$-\,2^{2}\cdot 101\cdot 49121$	$3$	$11.0286212826$	$4454.759701712315$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$9.48691886615$
7.1.19922352.1	$x^{7} - x^{6} - 4 x^{5} + 3 x^{4} + 4 x^{3} - x^{2} + 3 x + 4$	$7$	[1,3]	$-\,2^{4}\cdot 3\cdot 113\cdot 3673$	$4$	$11.0347613273$	$1771.319799196888$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$7.84420347741$
7.1.20021539.1	$x^{7} - x^{6} + 2 x^{3} - 5 x^{2} + 3 x - 1$	$7$	[1,3]	$-\,20021539$	$1$	$11.042592995$	$4474.54344039702$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.05414502562$
7.1.20057031.1	$x^{7} - 3 x^{6} + 4 x^{5} - 2 x^{4} - x^{3} - 2 x^{2} + 3 x - 1$	$7$	[1,3]	$-\,3^{3}\cdot 31^{2}\cdot 773$	$3$	$11.0453873162$	$988.4901362551063$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.64026898646$
7.1.20260912.1	$x^{7} - 2 x^{6} + 3 x^{5} - 5 x^{4} + 5 x^{3} + x^{2} + 2 x - 1$	$7$	[1,3]	$-\,2^{4}\cdot 7^{2}\cdot 43\cdot 601$	$4$	$11.061357458$	$933.8063458036289$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.50919029268$
7.1.20408504.1	$x^{7} - 2 x^{6} + 7 x^{5} - 9 x^{4} + 10 x^{3} - 6 x^{2} + 4 x - 1$	$7$	[1,3]	$-\,2^{3}\cdot 2551063$	$2$	$11.072832713$	$4517.577226788713$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$6.18943036704$
7.1.20417491.1	$x^{7} - 2 x^{6} + x^{5} - x^{4} + 4 x^{3} - 4 x^{2} + x - 1$	$7$	[1,3]	$-\,23\cdot 887717$	$2$	$11.0735291508$	$4518.571787633788$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$5.5335199126$
7.1.20550475.1	$x^{7} - 3 x^{6} + 6 x^{5} - 7 x^{4} + 7 x^{3} - x^{2} - x - 1$	$7$	[1,3]	$-\,5^{2}\cdot 11\cdot 74729$	$3$	$11.0838040113$	$2651.068386246601$	?	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$4.86491871386$
7.1.20590192.1	$x^{7} + 4 x^{5} - x^{4} + 3 x^{3} - 2 x^{2} + 1$	$7$	[1,3]	$-\,2^{4}\cdot 7^{2}\cdot 26263$	$3$	$11.0868616483$	$746.5264219086129$	✓	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$8.52126622661$

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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.