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 481)

Label	Polynomial	Discriminant	Galois group	Class group
5.1.471888729.2	x^5 - x^4 + x^3 - 24x^2 + 96x - 72	\( 3^{2}\cdot 13^{2}\cdot 557^{2} \)	$D_{5}$ (as 5T2)	$[121]$
5.1.10360232000.1	x^5 - 2x^4 - 55x^3 - 200x^2 - 430x - 640	\( 2^{6}\cdot 5^{3}\cdot 109^{3} \)	$F_5$ (as 5T3)	$[145]$
5.1.19172375352.1	x^5 - x^4 + 25x^3 - 90x^2 - 126x + 720	\( 2^{3}\cdot 3^{5}\cdot 13^{3}\cdot 67^{2} \)	$S_5$ (as 5T5)	$[219]$
5.1.22415542848.4	x^5 - x^4 + 7x^3 - 143x^2 + 134x - 146	\( 2^{6}\cdot 3^{2}\cdot 17^{3}\cdot 89^{2} \)	$F_5$ (as 5T3)	$[170]$
5.1.26881242025.1	x^5 - 2x^4 - 16x^3 - 97x^2 - 150x - 76	\( 5^{2}\cdot 11^{4}\cdot 271^{2} \)	$D_{5}$ (as 5T2)	$[145]$
5.1.27922744201.1	x^5 - x^4 + 29x^3 - 52x^2 + 377x - 1530	\( 11^{4}\cdot 1381^{2} \)	$A_5$ (as 5T4)	$[150]$
5.1.31266726976.1	x^5 - 93x^3 - 62x^2 + 2294x + 2108	\( 2^{6}\cdot 23^{2}\cdot 31^{4} \)	$D_{5}$ (as 5T2)	$[5, 25]$
5.1.38613822016.1	x^5 - 2x^4 + 61x^3 - 108x^2 + 554x - 912	\( 2^{6}\cdot 7^{2}\cdot 11^{4}\cdot 29^{2} \)	$D_{5}$ (as 5T2)	$[5, 25]$
5.1.47463076672.1	x^5 - 2x^4 + 72x^3 - 196x^2 - 865x - 3222	\( 2^{6}\cdot 11^{4}\cdot 37^{3} \)	$F_5$ (as 5T3)	$[5, 25]$
5.1.58505450641.1	x^5 - 2x^4 + 39x^3 - 75x^2 + 37x + 1	\( 11^{4}\cdot 1999^{2} \)	$D_{5}$ (as 5T2)	$[2, 110]$
5.1.82445359689.1	x^5 - x^4 + 18x^3 - 41x^2 + 3x + 505	\( 3^{2}\cdot 7^{2}\cdot 11^{4}\cdot 113^{2} \)	$A_5$ (as 5T4)	$[120]$
5.1.121945000000.8	x^5 + 75x^3 - 30x^2 - 1460x + 2568	\( 2^{6}\cdot 5^{7}\cdot 29^{3} \)	$F_5$ (as 5T3)	$[140]$
5.1.122265703125.1	x^5 - 30x^3 + 405x - 603	\( 3^{4}\cdot 5^{7}\cdot 139^{2} \)	$S_5$ (as 5T5)	$[140]$
5.1.172225000000.3	x^5 - 65x^3 - 90x^2 + 2060x + 568	\( 2^{6}\cdot 5^{8}\cdot 83^{2} \)	$D_{5}$ (as 5T2)	$[20, 20]$
5.1.282245496624.1	x^5 - x^4 + 34x^3 - 354x^2 - 1800x - 2196	\( 2^{4}\cdot 3^{4}\cdot 7^{3}\cdot 13^{3}\cdot 17^{2} \)	$S_5$ (as 5T5)	$[2, 72]$
5.1.298262478125.3	x^5 + 10x^3 - 105x^2 - 15x + 478	\( 5^{5}\cdot 457^{3} \)	$F_5$ (as 5T3)	$[285]$
5.1.350084039041.1	x^5 - x^4 - 49x^3 - 355x^2 - 924x - 1936	\( 11^{2}\cdot 19^{4}\cdot 149^{2} \)	$A_5$ (as 5T4)	$[120]$
5.1.366218625600.1	x^5 - 2x^4 + 18x^3 - 204x^2 + 705x - 450	\( 2^{6}\cdot 3^{4}\cdot 5^{2}\cdot 41^{4} \)	$A_5$ (as 5T4)	$[150]$
5.1.449307000000.1	x^5 - 15x^3 - 260x^2 + 1635x - 2178	\( 2^{6}\cdot 3^{5}\cdot 5^{6}\cdot 43^{2} \)	$S_5$ (as 5T5)	$[2, 60]$
5.1.505870703125.2	x^5 + 10x^3 - 115x^2 - 15x + 568	\( 5^{8}\cdot 109^{3} \)	$F_5$ (as 5T3)	$[10, 20]$
5.1.618582250000.1	x^5 + 110x^3 - 2420x^2 + 13805x - 26356	\( 2^{4}\cdot 5^{6}\cdot 11^{4}\cdot 13^{2} \)	$D_{5}$ (as 5T2)	$[5, 5, 5]$
5.1.646201250000.1	x^5 - 5x^3 + 5x - 2878	\( 2^{4}\cdot 5^{7}\cdot 719^{2} \)	$F_5$ (as 5T3)	$[220]$
5.1.658696183201.1	x^5 - x^4 + 43x^3 + 460x^2 - 1679x + 14696	\( 7^{2}\cdot 23^{2}\cdot 71^{4} \)	$A_5$ (as 5T4)	$[105]$
5.1.661951468816.1	x^5 - 2x^4 + 182x^3 - 614x^2 + 7429x + 452	\( 2^{4}\cdot 11^{4}\cdot 41^{4} \)	$A_5$ (as 5T4)	$[5, 60]$
5.1.715270753125.3	x^5 - 123	\( 3^{4}\cdot 5^{5}\cdot 41^{4} \)	$F_5$ (as 5T3)	$[5, 45]$
5.1.865361341504.1	x^5 + 1364x - 5456	\( 2^{6}\cdot 11^{4}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.865361341504.3	x^5 - 2x^4 + 138x^3 + 1036x^2 + 12137x + 18998	\( 2^{6}\cdot 11^{4}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.865361341504.4	x^5 - 2x^4 + 138x^3 + 1036x^2 - 2867x + 32638	\( 2^{6}\cdot 11^{4}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.1567962265489.1	x^5 - 2x^4 + 14x^3 - 49x^2 + 78x - 253	\( 31^{4}\cdot 1303^{2} \)	$A_5$ (as 5T4)	$[5, 45]$
5.1.1690158870125.3	x^5 - x^4 - 136x^3 - 1746x^2 - 10601x - 25642	\( 5^{3}\cdot 11^{4}\cdot 31^{4} \)	$F_5$ (as 5T3)	$[5, 30]$
5.1.1750045889449.1	x^5 - x^4 + 128x^3 - 217x^2 + 20023x + 25574	\( 11^{4}\cdot 13^{2}\cdot 29^{4} \)	$A_5$ (as 5T4)	$[5, 45]$
5.1.2028845000000.3	x^5 + 35x^3 + 875x - 910	\( 2^{6}\cdot 5^{7}\cdot 7^{4}\cdot 13^{2} \)	$S_5$ (as 5T5)	$[2, 80]$
5.1.2064609765625.2	x^5 - 165x^3 - 1815x^2 - 13640x - 53757	\( 5^{8}\cdot 11^{4}\cdot 19^{2} \)	$D_{5}$ (as 5T2)	$[5, 5, 5]$
5.1.2064609765625.3	x^5 - 165x^3 - 2860x^2 - 8415x - 18018	\( 5^{8}\cdot 11^{4}\cdot 19^{2} \)	$D_{5}$ (as 5T2)	$[5, 95]$
5.1.2530050082816.2	x^5 - x^4 + 184x^3 - 536x^2 + 11542x + 4930	\( 2^{11}\cdot 29^{3}\cdot 37^{3} \)	$S_5$ (as 5T5)	$[170]$
5.1.2769168200000.1	x^5 + 21350x - 57828	\( 2^{6}\cdot 5^{5}\cdot 61^{4} \)	$S_5$ (as 5T5)	$[130]$
5.1.2890571228224.3	x^5 - 2x^4 + 186x^3 + 1954x^2 + 9659x + 53404	\( 2^{6}\cdot 461^{4} \)	$A_5$ (as 5T4)	$[210]$
5.1.3137112050000.2	x^5 - 356	\( 2^{4}\cdot 5^{5}\cdot 89^{4} \)	$F_5$ (as 5T3)	$[4, 40]$
5.1.3294225000000.6	x^5 - 110x^3 - 330x^2 + 7535x + 30074	\( 2^{6}\cdot 3^{2}\cdot 5^{8}\cdot 11^{4} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.4240798862400.1	x^5 - 2x^4 - 339x^3 + 5428x^2 - 28910x + 58800	\( 2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 131^{4} \)	$D_{5}$ (as 5T2)	$[11, 55]$
5.1.4809797265625.1	x^5 + 165x^3 - 2530x^2 + 12760x - 22176	\( 5^{8}\cdot 11^{4}\cdot 29^{2} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.5772006250000.2	x^5 + 310x^3 - 1860x^2 + 7285x + 73532	\( 2^{4}\cdot 5^{8}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[15, 30]$
5.1.6194123253125.1	x^5 - 211	\( 5^{5}\cdot 211^{4} \)	$F_5$ (as 5T3)	$[5, 5, 5]$
5.1.7788252073536.4	x^5 - x^4 - 136x^3 + 3028x^2 + 12928x + 13232	\( 2^{6}\cdot 3^{2}\cdot 11^{4}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[5, 75]$
5.1.11459816005225.1	x^5 - x^4 + 498x^3 - 1157x^2 - 14097x + 46567	\( 5^{2}\cdot 7^{2}\cdot 311^{4} \)	$A_5$ (as 5T4)	$[120]$
5.1.11567205000000.1	x^5 + 4875x - 19500	\( 2^{6}\cdot 3^{4}\cdot 5^{7}\cdot 13^{4} \)	$S_5$ (as 5T5)	$[10, 20]$
5.1.11956498405489.1	x^5 - 902x^2 + 5863x - 2706	\( 11^{4}\cdot 17^{2}\cdot 41^{4} \)	$A_5$ (as 5T4)	$[5, 5, 30]$
5.1.12973885317184.4	x^5 - 2x^4 + 270x^3 + 3918x^2 - 381x + 88012	\( 2^{6}\cdot 11^{4}\cdot 61^{4} \)	$A_5$ (as 5T4)	$[5, 30]$
5.1.14288951250000.2	x^5 + 70x^3 + 980x - 1078	\( 2^{4}\cdot 3^{2}\cdot 5^{7}\cdot 7^{4}\cdot 23^{2} \)	$F_5$ (as 5T3)	$[5, 30]$
5.1.16563556927225.3	x^5 - x^4 - 477x^3 - 723x^2 + 70216x + 105984	\( 5^{2}\cdot 7^{2}\cdot 11^{4}\cdot 31^{4} \)	$A_5$ (as 5T4)	$[5, 60]$