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 41 matches)

Label	Polynomial	Discriminant	Galois group	Class group
13.1.48551226272641.1	x^13 - 2x^12 + 4x^10 - 5x^9 + x^8 + 5x^7 - 11x^6 + 19x^5 - 22x^4 + 16x^3 - 10x^2 + 6x - 1	\( 191^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.330928743953809.1	x^13 - 6x^12 + 15x^11 - 21x^10 + 19x^9 - 13x^8 + 12x^7 - 22x^6 + 36x^5 - 38x^4 + 27x^3 - 16x^2 + 8x - 1	\( 263^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.27983987175790801.1	x^13 - 4x^12 + 5x^11 - 2x^10 - 3x^9 - 3x^8 + 21x^7 + 3x^6 - 15x^5 - 15x^4 + 7x^3 + 25x^2 + 8x + 1	\( 19^{6}\cdot 29^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.50018670786022849.1	x^13 - 2x^12 + 3x^11 - x^10 - 7x^9 - 9x^8 + 21x^7 + 21x^6 - 3x^5 - 34x^4 - 16x^3 + 15x^2 + 17x - 1	\( 607^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.63121332085847281.1	x^13 - 4x^12 + 12x^11 - 21x^10 + 37x^9 - 46x^8 + 54x^7 - 72x^6 + 71x^5 - 77x^4 + 69x^3 - 33x^2 + 17x + 1	\( 631^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.147640825624179889.1	x^13 - 4x^12 + 8x^11 - 5x^10 + 6x^9 + 4x^7 + 8x^6 + 30x^5 - 15x^4 + 41x^3 - 23x^2 + 25x - 1	\( 727^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.739746811004793201.1	x^13 - 5x^12 + 10x^11 - 14x^10 + 13x^9 - 5x^8 - 22x^7 + 68x^6 - 118x^5 + 86x^4 + 32x^3 - 175x^2 + 165x - 117	\( 3^{6}\cdot 317^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.1119554149718639881.1	x^13 - 4x^12 + 17x^11 - 26x^10 + 51x^9 - 26x^8 + 43x^7 + 44x^6 - 21x^5 + 106x^4 - 15x^3 + 10x^2 + 48x - 32	\( 1019^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.3760094162052865729.1	x^13 - 5x^12 + 9x^11 - 5x^10 + 6x^9 - 56x^8 + 137x^7 - 132x^6 + 40x^5 + x^4 + 61x^3 - 85x^2 + 28x + 25	\( 29^{6}\cdot 43^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.3925887374183366656.1	x^13 - 6x^12 + 18x^11 - 32x^10 + 16x^9 + 64x^8 - 162x^7 + 96x^6 + 211x^5 - 394x^4 + 168x^3 + 136x^2 + 20x - 8	\( 2^{18}\cdot 157^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.8879014467287415361.1	x^13 - 6x^12 + 21x^11 - 51x^10 + 86x^9 - 124x^8 + 177x^7 - 203x^6 + 217x^5 - 230x^4 + 152x^3 - 163x^2 + 63x - 49	\( 1439^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.9332639163597796201.1	x^13 - 3x^12 + 24x^10 - 55x^9 + 3x^8 + 159x^7 - 451x^6 + 650x^5 - 808x^4 + 757x^3 - 681x^2 + 344x - 196	\( 1451^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.11345138370033741001.1	x^13 - 6x^12 + 19x^11 - 37x^10 + 60x^9 - 157x^8 + 503x^7 - 1154x^6 + 1645x^5 - 1339x^4 + 492x^3 - 315x^2 + 848x - 592	\( 1499^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.21459203535665809369.1	x^13 - 5x^12 - 2x^11 + 54x^10 - 98x^9 - 80x^8 + 441x^7 - 237x^6 - 814x^5 + 1060x^4 + 624x^3 - 336x^2 - 32x + 64	\( 1667^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.22402896724819285921.1	x^13 - 4x^12 + 17x^11 - 59x^10 + 147x^9 - 256x^8 + 356x^7 - 423x^6 + 457x^5 - 390x^4 + 253x^3 - 102x^2 + 63x + 19	\( 23^{6}\cdot 73^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.27277017024655140625.1	x^13 - 3x^12 - x^11 + 17x^9 + 28x^8 - 67x^7 - 137x^6 + 147x^5 + 140x^4 + 168x^3 - 803x^2 - 220x - 395	\( 5^{6}\cdot 347^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.37805311079775207424.1	x^13 - 6x^12 + 25x^11 - 84x^10 + 217x^9 - 478x^8 + 903x^7 - 1520x^6 + 2050x^5 - 2560x^4 + 2452x^3 - 1792x^2 + 552x - 160	\( 2^{18}\cdot 229^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.48095468356445867449.1	x^13 - x^12 + 15x^11 - 34x^10 + 93x^9 - 251x^8 + 394x^7 - 405x^6 + 245x^5 + 62x^4 - 509x^3 + 543x^2 - 271x + 374	\( 1907^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.93648472563048956281.1	x^13 - 5x^12 + 8x^11 + 5x^10 - 50x^9 + 175x^8 - 384x^7 + 399x^6 + 257x^5 - 1126x^4 + 856x^3 + 40x^2 - 1456x + 2048	\( 2131^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.96857448932353894849.1	x^13 - 5x^12 + 11x^11 - 8x^10 - 2x^9 - 46x^8 + 336x^7 - 876x^6 + 942x^5 + 304x^4 - 1784x^3 + 983x^2 + 828x - 657	\( 2143^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.115561720475814570049.1	x^13 - 4x^12 + 3x^11 - 26x^10 + 84x^9 - 134x^8 + 228x^7 - 448x^6 + 450x^5 - 559x^4 + 669x^3 - 463x^2 + 365x - 191	\( 2207^{6} \)	$D_{13}$ (as 13T2)	Trivial
13.1.177659863407592677721.1	x^13 - 3x^12 - 5x^11 + 43x^10 - 65x^9 - 83x^8 + 391x^7 - 461x^6 + 273x^5 + x^4 - 1395x^3 + 2727x^2 - 1620x + 324	\( 2371^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.353435381945484998041.1	x^13 - 6x^12 + 15x^11 - 18x^10 + 21x^9 - 68x^8 + 179x^7 + 110x^6 + 349x^5 - 2710x^4 + 4223x^3 - 3004x^2 + 1040x - 128	\( 2659^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.472671066694422108241.1	x^13 - 2x^12 + 3x^11 + 16x^10 - 47x^9 + 129x^8 + 24x^7 - 255x^6 + 1320x^5 - 1394x^4 + 1138x^3 + 156x^2 - 757x + 509	\( 2791^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.676690234146109500409.1	x^13 - x^12 + 4x^11 - 16x^10 - 47x^9 + 117x^8 - 474x^7 + 1302x^6 - 621x^5 + 173x^4 - 410x^3 + 880x^2 - 584x + 176	\( 2963^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.858699378083006947369.1	x^13 - 4x^12 + 12x^11 - 44x^10 + 113x^9 - 62x^8 + 317x^7 - 972x^6 + 1238x^5 - 1890x^4 + 1319x^3 - 2988x^2 + 9256x - 6616	\( 3083^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.1925008972063998217489.1	x^13 - 2x^12 - 3x^11 + 18x^10 + 24x^9 - 70x^8 - 62x^7 + 172x^6 + 334x^5 - 265x^4 - 1189x^3 - 971x^2 + 311x - 37	\( 3527^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.2528507645606750993641.1	x^13 - 6x^12 + 17x^11 - 25x^10 + 51x^9 - 65x^8 - 62x^7 + 849x^6 - 3034x^5 + 9140x^4 - 13920x^3 + 10576x^2 - 3936x + 576	\( 3691^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.2857417638294213107569.1	x^13 - 3x^12 + 6x^11 - x^10 + 56x^9 + 182x^8 + 564x^7 + 902x^6 + 1582x^5 + 2124x^4 + 2769x^3 + 2650x^2 + 3150x - 3625	\( 3767^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.3622860243332643912481.1	x^13 - 8x^11 - 9x^10 - 12x^9 + 108x^8 + 128x^7 + 78x^6 - 543x^5 - 582x^4 - 80x^3 + 771x^2 + 568x + 489	\( 3919^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.4114466594579445832729.1	x^13 - 3x^12 + 18x^10 - 6x^9 - 56x^8 + 152x^7 + 128x^6 + 256x^5 - 106x^4 - 370x^3 - 136x^2 - x - 5	\( 4003^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.4827084047654211776161.1	x^13 - 2x^12 - 14x^11 + 84x^10 - 189x^9 + 211x^8 - 212x^7 + 213x^6 + 230x^5 - 987x^4 + 1476x^3 - 783x^2 - 1296x + 1701	\( 4111^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.6069842589352832529121.1	x^13 - 11x^11 - 2x^10 + 108x^9 - 209x^8 + 478x^7 - 993x^6 + 1036x^5 - 990x^4 + 914x^3 + 258x^2 + 274x + 379	\( 4271^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.8381569459284757656649.1	x^13 - 6x^12 + 24x^11 - 65x^10 + 99x^9 - 132x^8 - 6x^7 - 225x^6 + 1034x^5 - 4692x^4 + 9024x^3 - 15040x^2 + 12288x - 9216	\( 4507^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.10018255465354231789849.1	x^13 - x^12 + 7x^11 - 48x^10 - 41x^9 + 135x^8 + 320x^7 - 521x^6 + 573x^5 + 1348x^4 + 633x^3 - 459x^2 - 181x - 166	\( 4643^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.10493449363391633467921.1	x^13 - 4x^12 - x^11 - 34x^10 + 227x^9 - 353x^8 + 1159x^7 - 4050x^6 + 5688x^5 - 5653x^4 - 1085x^3 + 1646x^2 - 1591x - 1093	\( 4679^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.11500326821733619716001.1	x^13 - 3x^12 - 12x^11 + 78x^10 - 110x^9 - 306x^8 + 1447x^7 - 2343x^6 + 1990x^5 - 1046x^4 + 128x^3 + 748x^2 - 316x + 373	\( 4751^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.13356995431497099192721.1	x^13 - 6x^12 + 9x^11 - 4x^10 + 107x^9 - 72x^8 - 26x^7 - 390x^6 + 213x^5 + 237x^4 - 462x^3 - 766x^2 - 459x - 103	\( 4871^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.1.14166446810699272506481.1	x^13 - x^12 - 8x^11 - 49x^10 - 69x^9 + 218x^8 + 1013x^7 + 3697x^6 + 11642x^5 + 26019x^4 + 35230x^3 + 27299x^2 + 10844x + 1813	\( 4919^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.13.282638808125771304198601.1	x^13 - 3x^12 - 41x^11 + 155x^10 + 376x^9 - 2028x^8 - 13x^7 + 8927x^6 - 7711x^5 - 13367x^4 + 20364x^3 + 1404x^2 - 13408x + 5312	\( 8101^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.13.361712403654141025034641.1	x^13 - x^12 - 50x^11 + 25x^10 + 722x^9 - 226x^8 - 4207x^7 + 1158x^6 + 10465x^5 - 2535x^4 - 9399x^3 + 1079x^2 + 1316x - 49	\( 23^{6}\cdot 367^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)