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 99)

Label	Polynomial	Discriminant	Galois group	Class group
20.18.132433392941210467352853142111.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 216x^16 + 300x^15 + 412x^14 - 1198x^13 + 62x^12 + 1890x^11 - 1091x^10 - 1327x^9 + 1343x^8 + 298x^7 - 689x^6 + 74x^5 + 166x^4 - 35x^3 - 20x^2 + 3x + 1	\( -\,37\cdot 6043\cdot 769611580061^{2} \)	20T1110	Trivial (GRH)
20.18.316110632872112441515151365391.1	x^20 - 10x^19 + 29x^18 + 24x^17 - 261x^16 + 252x^15 + 775x^14 - 1471x^13 - 832x^12 + 3315x^11 - 450x^10 - 3795x^9 + 2072x^8 + 2203x^7 - 2246x^6 - 562x^5 + 1187x^4 + 86x^3 - 275x^2 - 42x + 1	\( -\,661^{2}\cdot 38569^{4}\cdot 326951 \)	20T1015	Trivial (GRH)
20.18.470525233802978928640000000000.1	x^20 - 19x^18 + 136x^16 - 447x^14 + 624x^12 - 88x^10 - 640x^8 + 641x^6 - 240x^4 + 34x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.18.570917998018035498395055838671.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 216x^16 + 300x^15 + 415x^14 - 1219x^13 + 93x^12 + 1977x^11 - 1342x^10 - 1370x^9 + 1914x^8 + 87x^7 - 1224x^6 + 379x^5 + 367x^4 - 172x^3 - 38x^2 + 21x - 1	\( -\,3^{4}\cdot 19^{4}\cdot 37^{2}\cdot 2617^{4}\cdot 842279 \)	20T1015	Trivial (GRH)
20.18.610351562500000000000000000000.1	x^20 - 5x^18 - 25x^16 + 255x^14 - 825x^12 + 1374x^10 - 1285x^8 + 675x^6 - 190x^4 + 25x^2 - 1	\( -\,2^{20}\cdot 5^{34} \)	20T409	Trivial (GRH)
20.18.921574229218539911994717217859.1	x^20 - 10x^19 + 32x^18 - 3x^17 - 192x^16 + 312x^15 + 259x^14 - 1051x^13 + 364x^12 + 1365x^11 - 1319x^10 - 594x^9 + 1391x^8 - 239x^7 - 691x^6 + 293x^5 + 183x^4 - 77x^3 - 28x^2 + 4x + 1	\( -\,37^{2}\cdot 47^{2}\cdot 101\cdot 239^{2}\cdot 21391\cdot 1571417^{2} \)	20T1110	Trivial (GRH)
20.18.1342861649047383255040000000000.1	x^20 - 14x^18 + 77x^16 - 204x^14 + 232x^12 + 44x^10 - 386x^8 + 379x^6 - 154x^4 + 25x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 5471^{2}\cdot 66191^{2} \)	20T1045	Trivial (GRH)
20.18.1588027319649927224354711535616.1	x^20 - 16x^18 + 95x^16 - 240x^14 + 116x^12 + 658x^10 - 1438x^8 + 1227x^6 - 468x^4 + 65x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 5741^{2} \)	20T846	Trivial (GRH)
20.18.1657726634291894752305068359375.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 216x^16 + 300x^15 + 414x^14 - 1212x^13 + 84x^12 + 1940x^11 - 1247x^10 - 1339x^9 + 1675x^8 + 164x^7 - 990x^6 + 245x^5 + 280x^4 - 102x^3 - 33x^2 + 9x + 1	\( -\,5^{10}\cdot 1017319\cdot 408486641^{2} \)	20T1045	Trivial (GRH)
20.18.1950870747766649155582852857856.1	x^20 - 16x^18 + 91x^16 - 204x^14 + 41x^12 + 562x^10 - 946x^8 + 642x^6 - 195x^4 + 24x^2 - 1	\( -\,2^{40}\cdot 36497^{4} \)	20T992	Trivial (GRH)
20.18.1950870747766649155582852857856.2	x^20 - 20x^18 + 171x^16 - 816x^14 + 2379x^12 - 4356x^10 + 4949x^8 - 3304x^6 + 1140x^4 - 144x^2 - 1	\( -\,2^{40}\cdot 36497^{4} \)	20T992	Trivial (GRH)
20.18.2616374988854477216011959402496.1	x^20 - 15x^18 + 86x^16 - 222x^14 + 158x^12 + 468x^10 - 1211x^8 + 1137x^6 - 474x^4 + 72x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 7369^{2} \)	20T846	Trivial (GRH)
20.18.3370778611471959737030176850944.1	x^20 - 25x^18 + 196x^16 - 727x^14 + 1429x^12 - 1469x^10 + 631x^8 + 83x^6 - 156x^4 + 37x^2 - 1	\( -\,2^{10}\cdot 38569^{6} \)	20T808	Trivial (GRH)
20.18.3370778611471959737030176850944.2	x^20 - 19x^18 + 136x^16 - 447x^14 + 580x^12 + 236x^10 - 1302x^8 + 1046x^6 - 312x^4 + 33x^2 - 1	\( -\,2^{10}\cdot 38569^{6} \)	20T808	Trivial (GRH)
20.18.4862395450584134400640000000000.1	x^20 - 18x^18 + 130x^16 - 474x^14 + 873x^12 - 558x^10 - 629x^8 + 1349x^6 - 893x^4 + 236x^2 - 16	\( -\,2^{16}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.18.4862395450584134400640000000000.2	x^20 - 19x^18 + 124x^16 - 189x^14 - 1489x^12 + 8215x^10 - 16848x^8 + 15489x^6 - 5721x^4 + 604x^2 - 16	\( -\,2^{16}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.18.8455924749076998400000000000000.1	x^20 - 15x^18 + 70x^16 - 35x^14 - 720x^12 + 2599x^10 - 4075x^8 + 3255x^6 - 1275x^4 + 195x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T887	Trivial (GRH)
20.18.8455924749076998400000000000000.2	x^20 - 15x^18 + 84x^16 - 197x^14 + 46x^12 + 685x^10 - 1355x^8 + 1056x^6 - 333x^4 + 34x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T887	Trivial (GRH)
20.18.40230886178715161405440000000000.1	x^20 - 15x^18 + 67x^16 + 17x^14 - 954x^12 + 2868x^10 - 3604x^8 + 2016x^6 - 464x^4 + 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.18.40230886178715161405440000000000.2	x^20 - 14x^18 + 74x^16 - 170x^14 + 75x^12 + 429x^10 - 918x^8 + 770x^6 - 275x^4 + 30x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 211^{8} \)	20T647	Trivial (GRH)
20.18.59031562240000000000000000000000.1	x^20 - 15x^18 + 75x^16 - 90x^14 - 405x^12 + 1481x^10 - 1875x^8 + 1100x^6 - 305x^4 + 35x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.18.95749736674107392000000000000000.1	x^20 - 25x^18 + 181x^16 - 462x^14 - 11x^12 + 1929x^10 - 3269x^8 + 2330x^6 - 785x^4 + 115x^2 - 5	\( -\,2^{28}\cdot 5^{15}\cdot 43^{8} \)	20T513	Trivial (GRH)
20.18.110493290670952667151153400643584.1	x^20 - 14x^18 + 73x^16 - 165x^14 + 91x^12 + 282x^10 - 570x^8 + 420x^6 - 138x^4 + 20x^2 - 1	\( -\,2^{20}\cdot 397^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.18.112731072674656014761673622552576.1	x^20 - 16x^18 + 85x^16 - 107x^14 - 588x^12 + 2563x^10 - 4254x^8 + 3481x^6 - 1369x^4 + 206x^2 - 1	\( -\,2^{20}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.18.163023866649059818618082021484375.1	x^20 - 8x^19 + 3x^18 + 121x^17 - 246x^16 - 638x^15 + 2315x^14 + 1292x^13 - 10548x^12 - 804x^11 + 27547x^10 + 2633x^9 - 40347x^8 - 11191x^7 + 28572x^6 + 12631x^5 - 7548x^4 - 4002x^3 + 635x^2 + 320x - 29	\( -\,3^{8}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.18.211300041885398707129826254258176.1	x^20 - 21x^18 + 162x^16 - 626x^14 + 1336x^12 - 1593x^10 + 995x^8 - 254x^6 - 15x^4 + 15x^2 - 1	\( -\,2^{20}\cdot 3^{4}\cdot 61^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.18.1152137213317054324655456460800000.1	x^20 - 16x^18 + 9x^16 + 1175x^14 - 8820x^12 + 28288x^10 - 45494x^8 + 36516x^6 - 13830x^4 + 2253x^2 - 125	\( -\,2^{16}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.18.1166910956500388169989426463637504.1	x^20 - 22x^18 + 202x^16 - 1003x^14 + 2913x^12 - 4982x^10 + 4761x^8 - 2190x^6 + 308x^4 - 3x^2 - 1	\( -\,2^{26}\cdot 1429^{8} \)	20T849	Trivial (GRH)
20.18.1388569922790400000000000000000000.1	x^20 - 30x^18 + 320x^16 - 1640x^14 + 4540x^12 - 7056x^10 + 6040x^8 - 2560x^6 + 320x^4 + 80x^2 - 16	\( -\,2^{28}\cdot 5^{20}\cdot 7^{8}\cdot 97^{2} \)	20T946	Trivial (GRH)
20.18.1529709302460678995449698379104256.1	x^20 - 32x^18 + 397x^16 - 2513x^14 + 8896x^12 - 18053x^10 + 20368x^8 - 11083x^6 + 1263x^4 + 761x^2 - 1	\( -\,2^{28}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.18.1554923809853487093461057149075456.1	x^20 - 24x^18 + 231x^16 - 1137x^14 + 3006x^12 - 4005x^10 + 1858x^8 + 933x^6 - 959x^4 + 93x^2 - 1	\( -\,2^{20}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.18.2577947821925133337909357416991744.1	x^20 - 42x^18 + 618x^16 - 3789x^14 + 8961x^12 - 1682x^10 - 20616x^8 + 23886x^6 - 9370x^4 + 1235x^2 - 19	\( -\,2^{10}\cdot 19^{11}\cdot 43^{10} \)	20T423	Trivial (GRH)
20.18.2804604340661993478400000000000000.1	x^20 - 19x^18 + 148x^16 - 606x^14 + 1380x^12 - 1665x^10 + 814x^8 + 142x^6 - 234x^4 + 45x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 11^{4}\cdot 2339^{4} \)	20T1023	Trivial (GRH)
20.18.3912389503781481689907200000000000.1	x^20 - 19x^18 + 149x^16 - 622x^14 + 1482x^12 - 1986x^10 + 1316x^8 - 198x^6 - 179x^4 + 65x^2 - 5	\( -\,2^{32}\cdot 5^{11}\cdot 13^{4}\cdot 29^{4}\cdot 31^{4} \)	20T1036	Trivial (GRH)
20.18.6846284423532426067978240000000000.1	x^20 - 17x^18 + 75x^16 + 149x^14 - 2101x^12 + 6967x^10 - 11647x^8 + 10815x^6 - 5413x^4 + 1251x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.18.7372897256329164687850412645023744.1	x^20 - 33x^18 + 385x^16 - 1930x^14 + 4349x^12 - 4215x^10 + 871x^8 + 1026x^6 - 513x^4 + 43x^2 - 1	\( -\,2^{28}\cdot 13^{14}\cdot 17^{8} \)	20T803	Trivial (GRH)
20.18.8418205156916800000000000000000000.1	x^20 - 45x^18 + 780x^16 - 6720x^14 + 31575x^12 - 83559x^10 + 123340x^8 - 96640x^6 + 35500x^4 - 3880x^2 - 388	\( -\,2^{24}\cdot 5^{20}\cdot 7^{8}\cdot 97^{3} \)	20T946	Trivial (GRH)
20.18.9194738203964790047763420536341504.1	x^20 - 45x^18 + 639x^16 - 3014x^14 + 4891x^12 - 385x^10 - 5102x^8 + 4425x^6 - 1477x^4 + 203x^2 - 9	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.18.9194738203964790047763420536341504.2	x^20 - 40x^18 + 531x^16 - 3442x^14 + 12429x^12 - 26045x^10 + 31129x^8 - 19494x^6 + 5072x^4 - 171x^2 - 1	\( -\,2^{10}\cdot 17^{4}\cdot 401^{10} \)	20T852	Trivial (GRH)
20.18.9451143305862333221335953345347584.1	x^20 - 20x^18 + 92x^16 + 306x^14 - 3210x^12 + 7964x^10 - 8983x^8 + 5298x^6 - 1673x^4 + 264x^2 - 16	\( -\,2^{46}\cdot 7^{8}\cdot 13^{12} \)	20T633	Trivial (GRH)
20.18.14138200398183609412083027778994176.1	x^20 - 26x^18 + 221x^16 - 676x^14 - 841x^12 + 12122x^10 - 38070x^8 + 61118x^6 - 54233x^4 + 24884x^2 - 4489	\( -\,2^{40}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.18.14138200398183609412083027778994176.2	x^20 - 26x^18 + 254x^16 - 1204x^14 + 2954x^12 - 3696x^10 + 2047x^8 - 174x^6 - 212x^4 + 46x^2 - 1	\( -\,2^{40}\cdot 11^{16}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.18.15827379896489610792988840000000000.1	x^20 - 32x^18 + 350x^16 - 1763x^14 + 4019x^12 - 1163x^10 - 13305x^8 + 27140x^6 - 21088x^4 + 5888x^2 - 256	\( -\,2^{12}\cdot 5^{10}\cdot 13^{12}\cdot 19^{8} \)	20T633	Trivial (GRH)
20.18.17948300332081101479956111978679296.1	x^20 - 29x^18 + 233x^16 - 259x^14 - 2999x^12 + 11426x^10 - 16017x^8 + 10375x^6 - 3129x^4 + 418x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.18.18670575304006210719830823418200064.1	x^20 - 30x^18 + 243x^16 + 34x^14 - 9743x^12 + 53452x^10 - 128712x^8 + 151512x^6 - 81648x^4 + 16000x^2 - 256	\( -\,2^{30}\cdot 1429^{8} \)	20T849	Trivial (GRH)
20.18.19550982321594346663126636979348528.1	x^20 - 4x^19 - 12x^18 + 61x^17 + 51x^16 - 390x^15 - 66x^14 + 1357x^13 - 152x^12 - 2790x^11 + 638x^10 + 3442x^9 - 872x^8 - 2470x^7 + 533x^6 + 948x^5 - 123x^4 - 166x^3 + x^2 + 10x + 1	\( -\,2^{4}\cdot 7\cdot 2069\cdot 135002711\cdot 624953320648889659991 \)	20T1117	Trivial (GRH)
20.18.20562460332300807986799747065184256.1	x^20 - 46x^18 - 24x^17 + 806x^16 + 808x^15 - 6638x^14 - 9536x^13 + 25770x^12 + 49224x^11 - 41946x^10 - 120040x^9 + 13068x^8 + 139896x^7 + 20782x^6 - 76720x^5 - 12407x^4 + 16520x^3 + 2080x^2 - 992x - 62	\( -\,2^{48}\cdot 31^{7}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.18.30189084800892867773242735838887936.1	x^20 - 10x^19 + 25x^18 + 60x^17 - 344x^16 + 100x^15 + 1598x^14 - 1716x^13 - 3649x^12 + 5878x^11 + 4355x^10 - 9868x^9 - 2384x^8 + 9024x^7 - 2x^6 - 4412x^5 + 632x^4 + 1056x^3 - 248x^2 - 96x + 28	\( -\,2^{38}\cdot 23\cdot 809^{6}\cdot 17033 \)	20T955	Trivial (GRH)
20.18.38975590571565076699203650521995899.1	x^20 - 4x^19 - 12x^18 + 59x^17 + 55x^16 - 362x^15 - 119x^14 + 1200x^13 + 122x^12 - 2332x^11 - 73x^10 + 2694x^9 + 113x^8 - 1791x^7 - 174x^6 + 630x^5 + 106x^4 - 97x^3 - 22x^2 + 4x + 1	\( -\,162529\cdot 3567372786643\cdot 67222296673312217 \)	20T1117	Trivial (GRH)
20.18.112106138048743837664176950752575488.1	x^20 - 10x^19 + 23x^18 + 78x^17 - 381x^16 - 12x^15 + 2076x^14 - 1674x^13 - 5685x^12 + 7148x^11 + 8643x^10 - 14016x^9 - 7190x^8 + 14846x^7 + 2604x^6 - 8524x^5 + 333x^4 + 2492x^3 - 464x^2 - 288x + 81	\( -\,2^{20}\cdot 3^{10}\cdot 23^{4}\cdot 421\cdot 1451^{4}\cdot 3467 \)	20T1036	Trivial (GRH)