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 all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.59506232715491992087669.1	x^20 - x^19 + 3x^18 - 8x^17 + 16x^16 - 34x^15 + 39x^14 - 30x^13 - 3x^12 + 46x^11 - 57x^10 + 46x^9 - 3x^8 - 30x^7 + 39x^6 - 34x^5 + 16x^4 - 8x^3 + 3x^2 - x + 1	\( 11^{16}\cdot 109^{3} \)	20T303	Trivial
20.4.59506232715491992087669.2	x^20 - x^19 - 4x^18 + x^17 + 2x^16 - 6x^15 + 5x^14 + 20x^13 - 6x^12 - 39x^11 - 7x^10 + 55x^9 + 36x^8 - 47x^7 - 43x^6 + 21x^5 + 18x^4 - 8x^3 - 3x^2 + 3x + 1	\( 11^{16}\cdot 109^{3} \)	20T303	Trivial
20.6.1666352755035916574867251.1	x^20 - 5x^19 + 11x^18 - 19x^17 + 21x^16 - 14x^15 - 4x^14 + 33x^13 - 63x^12 + 88x^11 - 97x^10 + 88x^9 - 63x^8 + 33x^7 - 4x^6 - 14x^5 + 21x^4 - 19x^3 + 11x^2 - 5x + 1	\( -\,11^{16}\cdot 331^{3} \)	20T303	Trivial (GRH)
20.6.1666352755035916574867251.2	x^20 - 6x^19 + 17x^18 - 34x^17 + 52x^16 - 52x^15 + 14x^14 + 52x^13 - 105x^12 + 123x^11 - 123x^10 + 123x^9 - 105x^8 + 52x^7 + 14x^6 - 52x^5 + 52x^4 - 34x^3 + 17x^2 - 6x + 1	\( -\,11^{16}\cdot 331^{3} \)	20T303	Trivial (GRH)
20.6.17655750991471477605209863.1	x^20 - 2x^19 - 4x^18 + 11x^17 + 4x^16 - 32x^15 + 10x^14 + 84x^13 - 138x^12 + 18x^11 + 163x^10 - 146x^9 - 2x^8 + 43x^7 - 5x^6 + x^5 - 8x^4 - x^2 + x + 1	\( -\,11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.6.17655750991471477605209863.2	x^20 - 5x^19 + 3x^18 + 24x^17 - 54x^16 + 43x^15 - 25x^14 + 40x^13 - 60x^12 + 80x^11 - 93x^10 + 80x^9 - 60x^8 + 40x^7 - 25x^6 + 43x^5 - 54x^4 + 24x^3 + 3x^2 - 5x + 1	\( -\,11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.8.706993550892760357993595389.2	x^20 - 5x^19 - x^18 + 53x^17 - 113x^16 - 27x^15 + 483x^14 - 867x^13 + 592x^12 + 364x^11 - 1883x^10 + 4324x^9 - 6583x^8 + 5854x^7 - 2688x^6 + 1175x^5 - 1747x^4 + 1391x^3 - 72x^2 - 383x + 131	\( 11^{16}\cdot 109^{5} \)	20T303	Trivial (GRH)
20.8.706993550892760357993595389.3	x^20 + 3x^18 - 4x^17 - 19x^16 + 30x^15 - 25x^14 + 76x^13 + 61x^12 - 182x^11 + 72x^10 - 361x^9 + 685x^8 - 83x^7 - 808x^6 + 1015x^5 - 576x^4 - 234x^3 + 331x^2 - 26x - 23	\( 11^{16}\cdot 109^{5} \)	20T303	Trivial (GRH)
20.10.2136345869968048790230393423.1	x^20 - x^19 - 14x^18 + 18x^17 + 49x^16 - 88x^15 + 24x^14 + 196x^13 - 468x^12 - 239x^11 + 956x^10 + 78x^9 - 767x^8 + 202x^7 + 314x^6 - 22x^5 + 119x^4 + 35x^3 - 38x^2 - 3x + 1	\( -\,11^{18}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.10.2136345869968048790230393423.2	x^20 - 9x^19 + 42x^18 - 137x^17 + 332x^16 - 637x^15 + 947x^14 - 961x^13 + 382x^12 + 920x^11 - 2641x^10 + 3848x^9 - 3738x^8 + 2337x^7 - 607x^6 - 353x^5 + 406x^4 - 117x^3 - 30x^2 + 15x + 1	\( -\,11^{18}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.2.182567274194490055859030886811.1	x^20 - 2x^19 + 9x^18 - 31x^17 + 72x^16 - 155x^15 + 371x^14 - 593x^13 + 920x^12 - 1121x^11 + 810x^10 + 1297x^9 - 4485x^8 + 10655x^7 - 18446x^6 + 29415x^5 - 33613x^4 + 41746x^3 - 40635x^2 + 33365x - 11659	\( -\,11^{16}\cdot 331^{5} \)	20T303	$[2]$ (GRH)
20.10.182567274194490055859030886811.2	x^20 - 7x^19 + 21x^18 - 17x^17 - 105x^16 + 372x^15 - 387x^14 - 654x^13 + 2149x^12 - 1179x^11 - 2426x^10 + 3176x^9 + 2581x^8 + 452x^7 - 2075x^6 + 3150x^5 + 5979x^4 - 71x^3 - 833x^2 - 119x + 1	\( -\,11^{16}\cdot 331^{5} \)	20T303	Trivial (GRH)
20.2.182567274194490055859030886811.2	x^20 + 3x^18 - 5x^17 + 33x^16 - 23x^15 + 88x^14 - 201x^13 + 334x^12 - 798x^11 + 464x^10 - 2257x^9 - 219x^8 - 5621x^7 - 6131x^6 - 6021x^5 - 8743x^4 - 1563x^3 - 835x^2 - 3246x - 241	\( -\,11^{16}\cdot 331^{5} \)	20T303	$[2]$ (GRH)
20.10.182567274194490055859030886811.3	x^20 - 9x^19 + 28x^18 - 33x^17 + 32x^16 - 142x^15 + 161x^14 + 433x^13 - 718x^12 - 430x^11 + 211x^10 + 2199x^9 - 1895x^8 - 2702x^7 + 8059x^6 - 1473x^5 - 11463x^4 + 4686x^3 + 4857x^2 - 3056x + 397	\( -\,11^{16}\cdot 331^{5} \)	20T303	Trivial (GRH)
20.10.9331576415771428587203963681527.1	x^20 - 2x^19 - 17x^18 + 28x^17 + 49x^16 - 121x^15 + 237x^14 - 31x^13 - 1413x^12 + 2199x^11 + 328x^10 - 10864x^9 + 10725x^8 + 30897x^7 - 20987x^6 - 48171x^5 + 3738x^4 + 30453x^3 + 12300x^2 + 661x - 109	\( -\,11^{16}\cdot 727^{5} \)	20T303	Trivial (GRH)
20.10.9331576415771428587203963681527.2	x^20 - 6x^19 + 4x^18 + 48x^17 - 131x^16 - 68x^15 + 693x^14 - 240x^13 - 1531x^12 + 933x^11 + 682x^10 - 364x^9 + 2526x^8 - 8406x^7 + 2234x^6 + 19476x^5 - 12724x^4 - 6111x^3 + 2515x^2 - 4635x + 1277	\( -\,11^{16}\cdot 727^{5} \)	20T303	Trivial (GRH)
20.14.18513396751633196101360537305088.1	x^20 - 28x^18 + 342x^16 - 2347x^14 + 9824x^12 - 25779x^10 + 42159x^8 - 41028x^6 + 20803x^4 - 3219x^2 - 727	\( -\,2^{20}\cdot 11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.6.18513396751633196101360537305088.1	x^20 + 16x^18 + 67x^16 - 125x^14 - 1440x^12 - 2239x^10 + 4528x^8 + 17481x^6 + 16667x^4 + 2930x^2 - 727	\( -\,2^{20}\cdot 11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.14.18513396751633196101360537305088.2	x^20 - 20x^18 + 129x^16 - 177x^14 - 1382x^12 + 7269x^10 - 16076x^8 + 19707x^6 - 13789x^4 + 5066x^2 - 727	\( -\,2^{20}\cdot 11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.6.18513396751633196101360537305088.2	x^20 - 9x^18 - 50x^16 + 179x^14 + 1312x^12 + 1634x^10 - 3602x^8 - 11648x^6 - 11598x^4 - 4863x^2 - 727	\( -\,2^{20}\cdot 11^{16}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.20.19280067292868642604792128836993024.1	x^20 - 50x^18 + 986x^16 - 10331x^14 + 64059x^12 - 244682x^10 + 575732x^8 - 803006x^6 + 600924x^4 - 187263x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T303	Trivial (GRH)
20.20.19280067292868642604792128836993024.2	x^20 - 35x^18 + 511x^16 - 4084x^14 + 19737x^12 - 60231x^10 + 117640x^8 - 145311x^6 + 108566x^4 - 44164x^2 + 7369	\( 2^{20}\cdot 11^{16}\cdot 7369^{3} \)	20T303	Trivial (GRH)