Global number field search results

Further refine search

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 81)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.31337938340821894531250000.1	x^20 + x^18 - 7x^17 - 12x^16 - 21x^15 - 18x^14 - 11x^13 + 2x^12 + 15x^11 + 20x^10 + 15x^9 + 2x^8 - 11x^7 - 18x^6 - 21x^5 - 12x^4 - 7x^3 + x^2 + 1	\( -\,2^{4}\cdot 5^{13}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.10.3917242292602736816406250000.1	x^20 - 3x^19 + 4x^18 - 11x^17 - 5x^15 + 55x^14 + 47x^13 + 121x^12 - 418x^11 - 64x^10 + 708x^9 - 286x^8 - 453x^7 + 53x^6 + 267x^5 + 35x^4 - 65x^3 - 12x^2 + 5x + 1	\( -\,2^{4}\cdot 5^{16}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.4.12396113234941360655517578125.1	x^20 - 9x^18 + 44x^16 - 8x^15 - 134x^14 + 31x^13 + 228x^12 - 45x^11 - 164x^10 - 104x^9 - 166x^8 + 375x^7 + 340x^6 - 540x^5 - 35x^4 + 310x^3 - 190x^2 + 55x - 5	\( 5^{13}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.8.12396113234941360655517578125.1	x^20 - 2x^19 + 4x^18 - 5x^17 - 8x^16 + 11x^15 + 8x^14 - 69x^13 - 46x^12 + 529x^11 - 773x^10 - 94x^9 + 2655x^8 - 3046x^7 - 1350x^6 + 4388x^5 - 2179x^4 - 1522x^3 + 1135x^2 - 322x + 116	\( 5^{13}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.10.25672039088801296000000000000.1	x^20 - 10x^18 + 39x^16 - 105x^14 + 212x^12 - 109x^10 - 49x^8 - 158x^6 + 81x^4 + 4x^2 - 1	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.2.25672039088801296000000000000.1	x^20 + 7x^18 + 2x^16 - 56x^14 - 47x^12 + 149x^10 + 138x^8 - 64x^6 - 40x^4 - 8x^2 - 1	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.6.25672039088801296000000000000.1	x^20 - x^18 - 3x^16 - 27x^14 - 2x^12 + 3x^10 + 141x^8 + 59x^6 - 85x^4 - 24x^2 - 1	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.6.25672039088801296000000000000.2	x^20 - 7x^18 - 3x^16 + 82x^14 - 123x^12 - 278x^10 + 280x^8 + 236x^6 + 70x^4 - 78x^2 - 1	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.6.25672039088801296000000000000.3	x^20 + 4x^18 + 2x^16 + 14x^14 + 111x^12 + 119x^10 - 260x^8 - 343x^6 + 195x^4 + 168x^2 - 16	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.6.25672039088801296000000000000.4	x^20 - 3x^18 - 14x^16 + 69x^14 - 86x^12 - 30x^10 + 109x^8 - 95x^6 + 215x^4 - 100x^2 - 25	\( -\,2^{16}\cdot 5^{12}\cdot 6329^{4} \)	20T1037	Trivial (GRH)
20.4.39667562351812354097656250000.1	x^20 - 5x^19 + 18x^18 - 41x^17 + 77x^16 - 99x^15 + 97x^14 + 5x^13 - 181x^12 + 536x^11 - 870x^10 + 1361x^9 - 1588x^8 + 1721x^7 - 1708x^6 + 1208x^5 - 1055x^4 + 551x^3 - 284x^2 + 208x - 41	\( 2^{4}\cdot 5^{12}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.2.106589011856324768066406250000.1	x^20 - 10x^18 - 10x^17 + 30x^16 + 28x^15 - 35x^14 - 50x^13 - 25x^12 - 70x^11 + 63x^10 - 65x^9 + 100x^8 - 195x^7 - 5x^6 - 187x^5 + 125x^4 - 85x^3 + 165x^2 - 50x + 31	\( -\,2^{4}\cdot 5^{20}\cdot 7^{8}\cdot 59^{4} \)	20T1037	Trivial (GRH)
20.0.158670249407249416390625000000.1	x^20 + 10x^18 - 13x^17 + 32x^16 - 58x^15 + 72x^14 + 44x^13 + 31x^12 + 359x^11 - 774x^10 + 111x^9 + 1915x^8 - 1243x^7 - 892x^6 + 1548x^5 + 28x^4 - 274x^3 + 272x^2 - 154x + 61	\( 2^{6}\cdot 5^{12}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.2.181836148506250000000000000000.1	x^20 + 5x^16 + 10x^14 + 5x^12 + 29x^10 + 80x^8 + 75x^6 + 25x^4 - 1	\( -\,2^{16}\cdot 5^{20}\cdot 7^{4}\cdot 59^{4} \)	20T1037	Trivial (GRH)
20.0.198337811759061770488281250000.1	x^20 - 5x^19 + 16x^18 - 39x^17 + 77x^16 - 135x^15 + 179x^14 - 170x^13 + 137x^12 - 132x^11 + 180x^10 - 187x^9 + 105x^8 - 108x^7 + 159x^6 + 10x^5 + 33x^4 - 78x^3 + 10x^2 + 4x + 4	\( 2^{4}\cdot 5^{13}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.4.198337811759061770488281250000.1	x^20 - 5x^19 + 2x^18 + 30x^17 - 72x^16 + 74x^15 - 61x^14 + 64x^13 - 164x^12 + 981x^11 - 3040x^10 + 5226x^9 - 5690x^8 + 3098x^7 + 5233x^6 - 22521x^5 + 46207x^4 - 63712x^3 + 59290x^2 - 33464x + 8804	\( 2^{4}\cdot 5^{13}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.8.198337811759061770488281250000.1	x^20 - 7x^18 - 11x^17 - 59x^16 + 10x^15 + 358x^14 + 170x^13 - 623x^12 - 310x^11 + 820x^10 + 423x^9 - 487x^8 - 59x^7 + 377x^6 + 30x^5 - 125x^4 + 36x^3 + 28x^2 - 2x - 1	\( 2^{4}\cdot 5^{13}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.10.1337308814535692506945873248256.1	x^20 - 2x^19 - 11x^18 + 16x^17 + 53x^16 + 30x^15 - 289x^14 - 372x^13 + 897x^12 + 962x^11 - 717x^10 - 4904x^9 + 1807x^8 + 6930x^7 - 3827x^6 - 2724x^5 + 2626x^4 - 128x^3 - 532x^2 + 128x - 8	\( -\,2^{44}\cdot 31^{5}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.4.1549514154367670081939697265625.1	x^20 - x^18 - 2x^17 - 20x^15 - 90x^14 - 159x^13 + 123x^12 + 19x^11 - 389x^10 - 351x^9 + 5309x^8 + 1228x^7 - 7904x^6 + 21628x^5 - 9967x^4 - 1454x^3 + 3698x^2 + 1131x - 829	\( 5^{16}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.8.1549514154367670081939697265625.1	x^20 - 4x^19 + 4x^18 + 18x^17 - 64x^16 + 45x^15 + 98x^14 - 148x^13 - 573x^12 + 1458x^11 - 147x^10 - 4455x^9 + 7411x^8 - 1062x^7 - 7093x^6 + 8377x^5 - 99x^4 - 2554x^3 + 2477x^2 - 110x - 89	\( 5^{16}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.0.10728332761868750000000000000000.1	x^20 - 15x^18 + 65x^16 + 60x^14 - 1155x^12 + 2924x^10 - 2560x^8 + 685x^6 + 59	\( 2^{16}\cdot 5^{20}\cdot 7^{4}\cdot 59^{5} \)	20T1037	Trivial (GRH)
20.4.10728332761868750000000000000000.1	x^20 + 10x^18 + 25x^16 - 105x^14 - 795x^12 - 1781x^10 - 600x^8 + 2945x^6 + 1475x^4 - 3245x^2 + 59	\( 2^{16}\cdot 5^{20}\cdot 7^{4}\cdot 59^{5} \)	20T1037	Trivial (GRH)
20.0.10728332761868750000000000000000.2	x^20 + 5x^18 + 35x^16 + 155x^14 + 550x^12 + 1309x^10 + 1595x^8 + 945x^6 + 295x^4 + 59	\( 2^{16}\cdot 5^{20}\cdot 7^{4}\cdot 59^{5} \)	20T1037	Trivial (GRH)
20.4.10728332761868750000000000000000.2	x^20 - 5x^18 + 20x^16 - 65x^14 + 160x^12 - 336x^10 + 580x^8 - 725x^6 + 590x^4 - 295x^2 + 59	\( 2^{16}\cdot 5^{20}\cdot 7^{4}\cdot 59^{5} \)	20T1037	Trivial (GRH)
20.12.19833781175906177048828125000000.1	x^20 - 3x^19 - 22x^18 + 45x^17 + 197x^16 - 123x^15 - 867x^14 - 881x^13 + 1053x^12 + 5058x^11 + 4264x^10 - 3792x^9 - 10397x^8 - 13731x^7 - 4137x^6 + 6667x^5 + 8862x^4 + 17125x^3 + 7458x^2 - 293x - 109	\( 2^{6}\cdot 5^{15}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.14.21396941032571080111133971972096.1	x^20 - 6x^19 + x^18 + 32x^17 + 15x^16 + 14x^15 - 529x^14 - 336x^13 + 1941x^12 + 2834x^11 - 2933x^10 - 13636x^9 + 10409x^8 + 19254x^7 - 22425x^6 + 808x^5 + 11488x^4 - 10424x^3 + 2958x^2 + 948x - 446	\( -\,2^{48}\cdot 31^{5}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.12.24792226469882721311035156250000.1	x^20 - 22x^18 - 33x^17 + 91x^16 + 481x^15 + 918x^14 - 424x^13 - 5014x^12 - 10905x^11 - 12048x^10 + 4741x^9 + 38592x^8 + 69751x^7 + 82962x^6 + 58405x^5 + 12221x^4 - 11516x^3 - 9224x^2 - 2668x - 284	\( 2^{4}\cdot 5^{16}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.8.24792226469882721311035156250000.1	x^20 - 3x^19 + 2x^18 - 22x^17 + 23x^16 + 149x^15 - 164x^14 - 107x^13 - 639x^12 + 719x^11 + 3662x^10 - 4496x^9 - 6084x^8 + 7135x^7 + 10670x^6 - 5000x^5 - 15795x^4 + 780x^3 + 9445x^2 - 1570x - 745	\( 2^{4}\cdot 5^{16}\cdot 6329^{5} \)	20T1037	Trivial (GRH)
20.6.85587764130284320444535887888384.1	x^20 - 4x^18 - 20x^17 - 33x^16 - 8x^15 + 96x^14 + 484x^13 + 1272x^12 + 2344x^11 + 2252x^10 - 1580x^9 - 11586x^8 - 30456x^7 - 58856x^6 - 91508x^5 - 111125x^4 - 99528x^3 - 60976x^2 - 22704x - 3881	\( -\,2^{50}\cdot 31^{5}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.6.124070120141982925824000000000000.1	x^20 - x^18 - 9x^16 + 8x^14 + 39x^12 - 3x^10 - 75x^8 - 22x^6 + 51x^4 + 20x^2 - 4	\( -\,2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1037	Trivial (GRH)
20.6.124070120141982925824000000000000.2	x^20 + x^18 - 9x^16 - 8x^14 + 39x^12 + 3x^10 - 75x^8 + 22x^6 + 51x^4 - 20x^2 - 4	\( -\,2^{22}\cdot 3^{12}\cdot 5^{12}\cdot 691^{4} \)	20T1037	Trivial (GRH)
20.10.203105843888845487511469482421875.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 141x^16 + 312x^15 + 8x^14 - 722x^13 + 700x^12 + 376x^11 - 1066x^10 + 462x^9 + 409x^8 - 448x^7 + 64x^6 - 5x^5 + 38x^4 + 66x^3 - 45x^2 - 12x + 1	\( -\,3^{12}\cdot 5^{12}\cdot 691^{4}\cdot 1619\cdot 4241 \)	20T1037	Trivial (GRH)
20.4.404875324028746129193940673828125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 561x^16 - 1224x^15 + 2120x^14 - 2906x^13 + 3080x^12 - 2360x^11 + 1094x^10 - 130x^9 + 141x^8 - 960x^7 + 1688x^6 - 1657x^5 + 964x^4 - 270x^3 - 25x^2 + 40x + 5	\( 3^{12}\cdot 5^{12}\cdot 331\cdot 691^{4}\cdot 41351 \)	20T1037	Trivial (GRH)
20.8.978990791745334024080000000000000.1	x^20 - 14x^18 + 37x^16 + 200x^14 - 846x^12 - 676x^10 + 3874x^8 + 1320x^6 + 3085x^4 - 3390x^2 + 505	\( 2^{16}\cdot 3^{12}\cdot 5^{13}\cdot 101\cdot 691^{4} \)	20T1037	Trivial (GRH)
20.6.4538205239271006250000000000000000.1	x^20 - 10x^16 + 5x^14 + 30x^12 - 9x^10 - 65x^8 + 10x^6 + 75x^4 - 20x^2 - 16	\( -\,2^{16}\cdot 5^{20}\cdot 29^{4}\cdot 179^{4} \)	20T1037	Trivial (GRH)
20.12.4991699275727550043990996300070912.1	x^20 - 14x^18 + 62x^16 - 16x^15 - 104x^14 + 196x^13 + 177x^12 - 696x^11 - 770x^10 + 728x^9 + 1382x^8 + 56x^7 - 900x^6 - 348x^5 + 242x^4 + 168x^3 - 16x - 2	\( 2^{54}\cdot 31^{4}\cdot 113\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.8.4991699275727550043990996300070912.1	x^20 + 4x^18 - x^16 - 16x^15 - 88x^14 - 116x^13 - 221x^12 - 400x^11 - 516x^10 - 388x^9 - 193x^8 - 248x^7 + 116x^6 + 824x^5 + 786x^4 + 88x^3 - 200x^2 - 56x + 2	\( 2^{54}\cdot 31^{4}\cdot 113\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.0.5047029739577858513663735595703125.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1047x^16 - 3072x^15 + 7568x^14 - 15842x^13 + 28462x^12 - 44048x^11 + 58874x^10 - 67908x^9 + 67711x^8 - 58408x^7 + 44248x^6 - 29867x^5 + 18704x^4 - 10632x^3 + 5391x^2 - 1992x + 496	\( 3^{12}\cdot 5^{12}\cdot 71\cdot 691^{4}\cdot 2403091 \)	20T1037	Trivial (GRH)
20.14.5140615083075201996699936766296064.1	x^20 - 4x^19 - 22x^18 + 84x^17 + 194x^16 - 604x^15 - 1036x^14 + 1492x^13 + 5001x^12 + 552x^11 - 20502x^10 - 3352x^9 + 48973x^8 - 12160x^7 - 54194x^6 + 34260x^5 + 16936x^4 - 20996x^3 + 5824x^2 - 456x - 9	\( -\,2^{46}\cdot 31^{7}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.14.5140615083075201996699936766296064.2	x^20 - 2x^19 - 19x^18 - 4x^17 + 213x^16 + 302x^15 - 1179x^14 - 2868x^13 + 6790x^12 + 8088x^11 - 29132x^10 - 6536x^9 + 60204x^8 + 1444x^7 - 49614x^6 + 648x^5 + 14584x^4 + 160x^3 - 1032x^2 - 128x - 4	\( -\,2^{46}\cdot 31^{7}\cdot 227^{4} \)	20T1037	Trivial (GRH)
20.10.5583155406389231662080000000000000.1	x^20 - 18x^18 + 133x^16 - 510x^14 + 1019x^12 - 717x^10 - 1059x^8 + 2775x^6 - 2565x^4 + 1170x^2 - 180	\( -\,2^{22}\cdot 3^{14}\cdot 5^{13}\cdot 691^{4} \)	20T1037	Trivial (GRH)
20.2.5583155406389231662080000000000000.1	x^20 + 18x^18 + 133x^16 + 510x^14 + 1019x^12 + 717x^10 - 1059x^8 - 2775x^6 - 2565x^4 - 1170x^2 - 180	\( -\,2^{22}\cdot 3^{14}\cdot 5^{13}\cdot 691^{4} \)	20T1037	$[2]$ (GRH)
20.12.10138470020238062156310415283203125.1	x^20 - 10x^19 + 24x^18 + 69x^17 - 357x^16 + 1904x^14 - 1394x^13 - 5530x^12 + 5776x^11 + 10202x^10 - 11284x^9 - 13233x^8 + 11928x^7 + 12488x^6 - 6211x^5 - 7676x^4 + 696x^3 + 2207x^2 + 400x - 64	\( 3^{12}\cdot 5^{12}\cdot 691^{4}\cdot 342740261 \)	20T1037	Trivial (GRH)
20.4.15663852667925344385280000000000000.1	x^20 + 14x^18 + 37x^16 - 200x^14 - 846x^12 + 676x^10 + 3874x^8 - 1320x^6 + 3085x^4 + 3390x^2 + 505	\( 2^{20}\cdot 3^{12}\cdot 5^{13}\cdot 101\cdot 691^{4} \)	20T1037	Trivial (GRH)
20.10.20562460332300807986799747065184256.1	x^20 - 26x^18 - 20x^17 + 303x^16 + 436x^15 - 2442x^14 - 4456x^13 + 13882x^12 + 28708x^11 - 38018x^10 - 123496x^9 - 6466x^8 + 325044x^7 + 170086x^6 - 455176x^5 - 33791x^4 + 327188x^3 - 199392x^2 - 98868x + 76807	\( -\,2^{48}\cdot 31^{7}\cdot 227^{4} \)	20T1037	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)
20.2.20562460332300807986799747065184256.1	x^20 - 8x^19 + 34x^18 - 128x^17 + 423x^16 - 1156x^15 + 2910x^14 - 7024x^13 + 15179x^12 - 29364x^11 + 59722x^10 - 102224x^9 + 163695x^8 - 280712x^7 + 390516x^6 - 438328x^5 + 607404x^4 - 546072x^3 + 321288x^2 - 84952x + 6862	\( -\,2^{48}\cdot 31^{7}\cdot 227^{4} \)	20T1037	$[2, 2, 4]$ (GRH)
20.6.20562460332300807986799747065184256.1	x^20 + 8x^18 - 4x^17 + 197x^16 - 640x^15 - 184x^14 + 2424x^13 - 8218x^12 + 18088x^11 - 25840x^10 + 51592x^9 - 109238x^8 + 143472x^7 - 109512x^6 + 22904x^5 + 54417x^4 - 80120x^3 + 29960x^2 + 18092x - 3671	\( -\,2^{48}\cdot 31^{7}\cdot 227^{4} \)	20T1037	$[2]$ (GRH)
20.6.20562460332300807986799747065184256.2	x^20 - 4x^19 + 26x^18 - 72x^17 + 122x^16 + 52x^15 - 1462x^14 + 2088x^13 - 2936x^12 - 3448x^11 - 1864x^10 + 52944x^9 - 32472x^8 - 51840x^7 + 174368x^6 - 162304x^5 + 88512x^4 - 10624x^3 - 31872x^2 + 64768x - 33664	\( -\,2^{48}\cdot 31^{7}\cdot 227^{4} \)	20T1037	$[2]$ (GRH)
20.8.61571735716086245423376000000000000.1	x^20 - 6x^18 - 35x^16 + 264x^14 + 50x^12 - 2388x^10 + 786x^8 + 11688x^6 - 5427x^4 - 32598x^2 + 31761	\( 2^{16}\cdot 3^{14}\cdot 5^{12}\cdot 691^{4}\cdot 3529 \)	20T1037	Trivial (GRH)