Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 224)

Label	Polynomial	Discriminant	Galois group	Class group
7.1.7845011803.1	x^7 - 3x^6 + 5x^5 - 8x^4 + 55x^3 - 131x^2 + 147x - 18	\( -\,1987^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.8096384512.1	x^7 - 3x^6 + 6x^5 - 14x^4 + 15x^3 - x^2 + 82x - 134	\( -\,2^{9}\cdot 251^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.56225905191.1	x^7 - 2x^6 + 7x^5 - 20x^4 + 103x^3 + 112x^2 + 111x + 51	\( -\,3^{3}\cdot 1277^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.58575010032.2	x^7 - 3x^6 + 14x^5 - 28x^4 + 40x^3 - 104x^2 + 96x + 128	\( -\,2^{4}\cdot 3^{6}\cdot 7^{3}\cdot 11^{4} \)	$S_7$ (as 7T7)	$[11]$
7.1.63425726272.1	x^7 - x^6 + 7x^5 + x^4 + 116x^3 + 44x^2 + 272x + 96	\( -\,2^{6}\cdot 997^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.207029048256.1	x^7 - x^6 + 15x^5 - 17x^4 + 23x^3 - 9x^2 + 5x + 1	\( -\,2^{6}\cdot 3^{8}\cdot 79^{3} \)	$F_7$ (as 7T4)	$[14]$
7.1.243906324992.1	x^7 - 2x^6 + 4x^5 - 40x^4 + 196x^3 - 648x^2 + 1056x - 704	\( -\,2^{9}\cdot 11^{3}\cdot 71^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.247200192576.1	x^7 - 3x^6 + 4x^5 + 18x^4 - 53x^3 + 87x^2 - 72x + 162	\( -\,2^{6}\cdot 3^{3}\cdot 523^{3} \)	$D_{7}$ (as 7T2)	$[43]$
7.1.291698067968.1	x^7 - 3x^6 - 4x^5 + 40x^4 - 53x^3 - 77x^2 + 328x - 200	\( -\,2^{9}\cdot 829^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.467107946479.1	x^7 - 3x^6 + 20x^5 - 105x^4 + 234x^3 - 362x^2 + 545x - 425	\( -\,7759^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.489117612439.1	x^7 - 3x^6 + 3x^5 + 16x^4 - 80x^3 - 15x^2 + 90x - 551	\( -\,7879^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.648337611375.1	x^7 - x^6 - 5x^5 + 14x^4 - 98x^3 + 155x^2 - 78x + 417	\( -\,3^{3}\cdot 5^{3}\cdot 577^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.757303595875.1	x^7 - 3x^6 + 9x^5 - 10x^4 + 16x^3 + 344x^2 + 1040x + 960	\( -\,5^{3}\cdot 1823^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.1722980109375.2	x^7 - 3x^6 - 9x^5 + 120x^4 - 480x^3 + 1101x^2 - 1268x + 561	\( -\,3^{8}\cdot 5^{6}\cdot 7^{5} \)	$F_7$ (as 7T4)	$[14]$
7.3.1865365934656.1	x^7 - 2x^6 + 10x^5 - 2x^4 - 16x^3 + 16x^2 + 4x - 12	\( 2^{6}\cdot 7^{2}\cdot 29^{6} \)	$\GL(3,2)$ (as 7T5)	$[14]$
7.1.1962515008000.1	x^7 - 2x^6 - 15x^5 + 8x^4 + 258x^3 + 768x^2 + 400x - 2560	\( -\,2^{9}\cdot 5^{3}\cdot 313^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.2843371995463.1	x^7 + 13x^5 - 71x^4 + 25x^3 + 192x^2 - 50x - 275	\( -\,31^{3}\cdot 457^{3} \)	$D_{7}$ (as 7T2)	$[41]$
7.1.3053042381843.1	x^7 + 9x^5 - 78x^4 - 17x^3 + 150x^2 + 196x - 344	\( -\,89^{3}\cdot 163^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.3372300719936.1	x^7 - 3x^6 + 10x^5 - 50x^4 + 89x^3 + 189x^2 - 868x + 1144	\( -\,2^{6}\cdot 23^{3}\cdot 163^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.3437481658688.1	x^7 - 14x^5 - 42x^4 + 329x^3 + 854x^2 + 336x - 464	\( -\,2^{6}\cdot 7^{9}\cdot 11^{3} \)	$D_{7}$ (as 7T2)	$[43]$
7.3.3543369523456.4	x^7 - 21x^5 - 70x^4 + 238x^3 + 1092x^2 - 2240x + 736	\( 2^{8}\cdot 7^{12} \)	$\GL(3,2)$ (as 7T5)	$[14]$
7.1.6807097609375.1	x^7 - 35x^4 + 70x^3 - 70x + 35	\( -\,5^{6}\cdot 7^{7}\cdot 23^{2} \)	$S_7$ (as 7T7)	$[12]$
7.1.7143337990979.1	x^7 - 3x^6 - 30x^5 + 230x^4 - 471x^3 + 269x^2 - 268x + 784	\( -\,19259^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.7597737208179.1	x^7 - 3x^6 + 17x^5 - 76x^4 + 99x^3 - 839x^2 + 5355x - 6858	\( -\,3^{3}\cdot 6553^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.8202077997463.1	x^7 - 2x^6 + 8x^5 - 50x^4 + 99x^3 - 105x^2 - 61x - 21	\( -\,7^{3}\cdot 43^{3}\cdot 67^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.8559770978816.1	x^7 - 3x^6 - 9x^5 - 21x^4 + 554x^3 - 938x^2 - 608x - 328	\( -\,2^{9}\cdot 2557^{3} \)	$D_{7}$ (as 7T2)	$[71]$
7.1.8818423496000.1	x^7 - x^6 + 13x^5 - 173x^4 + 456x^3 - 56x^2 - 880x - 1360	\( -\,2^{6}\cdot 5^{3}\cdot 1033^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.9333955741375.1	x^7 - 3x^6 - 3x^5 + 108x^4 - 119x^3 - 1435x^2 + 3355x - 761	\( -\,5^{3}\cdot 4211^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.9397938459727.1	x^7 - 32x^5 - 70x^4 + 532x^3 + 750x^2 - 1727x - 5149	\( -\,47^{3}\cdot 449^{3} \)	$D_{7}$ (as 7T2)	$[43]$
7.1.9760921523136.1	x^7 + 14x^5 + 56x^3 + 56x - 286	\( -\,2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 19^{3} \)	$F_7$ (as 7T4)	$[21]$
7.1.10354530166336.1	x^7 - 3x^6 + 38x^5 + 30x^4 + 33x^3 + 1957x^2 - 2116x + 5956	\( -\,2^{6}\cdot 5449^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.10927746713871.1	x^7 - 5x^5 - 54x^4 - 20x^3 - 483x^2 - 2259x - 2187	\( -\,3^{3}\cdot 13^{3}\cdot 569^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.11328469648579.1	x^7 - 3x^6 - 26x^5 - 64x^4 - 170x^3 - 222x^2 - 41x - 331	\( -\,37^{3}\cdot 607^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.12135287592000.1	x^7 - 2x^6 - 11x^5 + 52x^4 - 236x^3 + 712x^2 - 1644x + 2928	\( -\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 383^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.12184465350331.1	x^7 - 2x^6 - 4x^5 - 78x^4 - 146x^3 - 408x^2 - 375x - 512	\( -\,23011^{3} \)	$D_{7}$ (as 7T2)	$[3, 3, 3]$
7.1.12280025186911.1	x^7 - 2x^6 - 18x^5 + 81x^4 - 233x^3 + 523x^2 - 462x + 657	\( -\,23071^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.3.13519130324569.2	x^7 - 8x^5 - 25x^4 - 17x^3 + 32x^2 + 96x + 64	\( 631^{2}\cdot 5827^{2} \)	$\GL(3,2)$ (as 7T5)	$[2, 10]$
7.1.16253878339691.1	x^7 - 3x^6 + 2x^5 + 65x^4 - 61x^3 + 216x^2 - 616x + 472	\( -\,73^{3}\cdot 347^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.17347830539103.1	x^7 - 3x^6 + 25x^5 + 36x^4 + 4x^3 + 387x^2 - 222x + 459	\( -\,3^{3}\cdot 8629^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.23568314355711.1	x^7 - x^6 - 26x^5 - 17x^4 + 188x^3 + 145x^2 + 1638x + 621	\( -\,3^{3}\cdot 19^{3}\cdot 503^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.3.23792932840000.4	x^7 - 2x^6 + 10x^5 - 2x^4 - 45x^3 - 564x^2 + 236x + 1496	\( 2^{6}\cdot 5^{4}\cdot 29^{6} \)	$\GL(3,2)$ (as 7T5)	$[14]$
7.1.23917744283328.3	x^7 - 196x^4 + 196x^3 - 784	\( -\,2^{6}\cdot 3^{3}\cdot 7^{12} \)	$S_7$ (as 7T7)	$[21]$
7.1.24054977590363.1	x^7 - 26x^5 - x^4 + 562x^3 - 1776x^2 + 3256x - 5680	\( -\,28867^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.24097501111104.1	x^7 - 2x^6 + 25x^5 - 110x^4 - 596x^3 - 920x^2 - 732x - 504	\( -\,2^{6}\cdot 3^{3}\cdot 29^{3}\cdot 83^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.25503049887875.1	x^7 - 2x^6 + 10x^5 - 118x^4 + 42x^3 + 770x^2 - 1127x - 3724	\( -\,5^{3}\cdot 7^{3}\cdot 29^{6} \)	$D_{7}$ (as 7T2)	$[91]$
7.1.30755498437691.1	x^7 - 3x^6 - 8x^5 - 52x^4 - 68x^3 - 136x^2 + 4335x + 19363	\( -\,17^{3}\cdot 19^{3}\cdot 97^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.31360177055375.1	x^7 - 3x^6 - 16x^5 - 18x^4 + 330x^3 - 354x^2 - 630x - 185	\( -\,5^{3}\cdot 7^{3}\cdot 17^{3}\cdot 53^{3} \)	$D_{7}$ (as 7T2)	$[29]$
7.1.31915344448000.1	x^7 - x^6 - 8x^5 - 72x^4 + 351x^3 - 91x^2 - 3380	\( -\,2^{9}\cdot 5^{3}\cdot 13^{3}\cdot 61^{3} \)	$D_{7}$ (as 7T2)	$[13]$
7.1.35427446793216.3	x^7 - 2x^6 - 12x^5 + 35x^4 - 4x^3 + 60x^2 - 416x + 484	\( -\,2^{10}\cdot 3^{6}\cdot 83^{4} \)	$S_7$ (as 7T7)	$[20]$
7.3.36299468209216.1	x^7 - 2x^6 + 22x^5 - 48x^4 + 136x^3 - 236x^2 + 130x - 2	\( 2^{6}\cdot 191^{2}\cdot 3943^{2} \)	$\GL(3,2)$ (as 7T5)	$[12]$