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 2289)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.35692254368051412309695449.1	x^20 - 13x^18 - 8x^17 + 28x^16 + 9x^15 - 18x^14 + 47x^13 + 73x^12 - 54x^11 - 155x^10 - 54x^9 + 73x^8 + 47x^7 - 18x^6 + 9x^5 + 28x^4 - 8x^3 - 13x^2 + 1	\( 61^{6}\cdot 167^{2}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.12.46148208848672993541568441.1	x^20 - x^19 - 6x^18 + 13x^17 - 4x^16 - 21x^15 - 17x^14 + 65x^13 + 252x^12 - 674x^11 + 87x^10 + 1178x^9 - 1094x^8 - 343x^7 + 983x^6 - 397x^5 - 148x^4 + 177x^3 - 54x^2 + 3x + 1	\( 11^{18}\cdot 43^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.12.49338146756019243307761664.1	x^20 - 8x^19 + 26x^18 - 40x^17 + 14x^16 + 76x^15 - 296x^14 + 658x^13 - 577x^12 - 362x^11 + 906x^10 - 866x^9 + 2214x^8 - 3458x^7 + 1784x^6 + 564x^5 - 1042x^4 + 542x^3 - 158x^2 + 22x - 1	\( 2^{30}\cdot 11^{16} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial (GRH)
20.12.49338146756019243307761664.2	x^20 - 4x^19 - 4x^18 + 24x^17 + 18x^16 - 92x^15 - 52x^14 + 388x^13 - 411x^12 - 122x^11 + 92x^10 + 1352x^9 - 1651x^8 - 314x^7 + 986x^6 + 46x^5 - 275x^4 - 14x^3 + 32x^2 + 2x - 1	\( 2^{30}\cdot 11^{16} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial (GRH)
20.12.103745853703303712158203125.1	x^20 - x^19 - 5x^18 + 7x^17 - 13x^16 - 18x^15 + 90x^14 - 28x^13 - 89x^12 + 219x^11 - 175x^10 - 400x^9 + 452x^8 + 355x^7 - 406x^6 - 186x^5 + 178x^4 + 61x^3 - 34x^2 - 10x + 1	\( 5^{13}\cdot 419^{2}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.12.119834225764331755130589184.1	x^20 - 20x^18 + 163x^16 - 717x^14 + 1904x^12 - 3263x^10 + 3779x^8 - 2996x^6 + 1540x^4 - 441x^2 + 49	\( 2^{12}\cdot 7^{6}\cdot 137^{4}\cdot 163^{4} \)	20T568	Trivial (GRH)
20.12.160508627161048272206823424.1	x^20 - 2x^19 - 16x^18 + 42x^17 + 57x^16 - 216x^15 + 38x^14 + 88x^13 + 368x^12 - 270x^11 - 388x^10 + 28x^9 + 583x^8 - 94x^7 - 568x^6 + 416x^5 + 27x^4 - 152x^3 + 72x^2 - 14x + 1	\( 2^{30}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4} \)	20T669	Trivial (GRH)
20.12.201604956366467437744140625.1	x^20 - 5x^19 + 45x^17 - 85x^16 - 50x^15 + 380x^14 - 470x^13 - 185x^12 + 1120x^11 - 1151x^10 + 140x^9 + 880x^8 - 1085x^7 + 545x^6 + 75x^5 - 320x^4 + 235x^3 - 85x^2 + 15x - 1	\( 5^{16}\cdot 6029^{4} \)	20T279	Trivial (GRH)
20.12.201707501835641831643973969.1	x^20 - 10x^19 + 41x^18 - 84x^17 + 45x^16 + 252x^15 - 850x^14 + 1336x^13 - 999x^12 - 350x^11 + 1777x^10 - 1950x^9 + 722x^8 + 652x^7 - 988x^6 + 420x^5 + 100x^4 - 172x^3 + 35x^2 + 22x - 1	\( 61^{6}\cdot 397^{6} \)	20T281	Trivial (GRH)
20.12.217008357018762359619140625.1	x^20 - 5x^19 + 35x^17 - 45x^16 - 66x^15 + 175x^14 + 5x^13 - 280x^12 + 75x^11 + 297x^10 - 75x^9 - 280x^8 - 5x^7 + 175x^6 + 66x^5 - 45x^4 - 35x^3 + 5x + 1	\( 3^{4}\cdot 5^{16}\cdot 23^{4}\cdot 89^{4} \)	20T279	Trivial (GRH)
20.12.303303398211110919797211136.1	x^20 - 5x^18 + 6x^16 + 2x^14 - 9x^10 + 2x^6 + 6x^4 - 5x^2 + 1	\( 2^{20}\cdot 29^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.328077615685375622346297241.1	x^20 - 7x^19 + 12x^18 + 6x^17 - 32x^16 + 51x^15 - 12x^14 - 151x^13 + 57x^12 + 203x^11 - 53x^10 - 203x^9 + 57x^8 + 151x^7 - 12x^6 - 51x^5 - 32x^4 - 6x^3 + 12x^2 + 7x + 1	\( 7^{8}\cdot 53^{4}\cdot 139^{6} \)	20T669	Trivial (GRH)
20.12.333344467865374796821005421.1	x^20 - 2x^19 - 16x^18 + 24x^17 + 96x^16 - 30x^15 - 360x^14 - 336x^13 + 617x^12 + 1473x^11 + 174x^10 - 2098x^9 - 1732x^8 + 763x^7 + 1463x^6 + 152x^5 - 412x^4 - 67x^3 + 49x^2 + x - 1	\( 7^{4}\cdot 137^{4}\cdot 163^{4}\cdot 179\cdot 3119 \)	20T992	Trivial (GRH)
20.12.336186938823068443362886656.1	x^20 - 8x^18 + 9x^16 + 49x^14 - 84x^12 - 43x^10 + 124x^8 - 35x^6 - 17x^4 + 4x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T262	Trivial (GRH)
20.12.336186938823068443362886656.2	x^20 - 5x^18 - 8x^16 + 73x^14 - 68x^12 - 166x^10 + 324x^8 - 146x^6 - 18x^4 + 13x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.336186938823068443362886656.3	x^20 - 4x^18 - 17x^16 + 68x^14 + 69x^12 - 298x^10 + 26x^8 + 358x^6 - 211x^4 + 8x^2 + 1	\( 2^{10}\cdot 3^{10}\cdot 11^{18} \)	20T340	Trivial (GRH)
20.12.343928789838259679743554901.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 134x^16 + 256x^15 + 140x^14 - 666x^13 + 58x^12 + 952x^11 - 245x^10 - 915x^9 + 220x^8 + 606x^7 - 73x^6 - 260x^5 - 5x^4 + 66x^3 + 4x^2 - 8x + 1	\( 101\cdot 277^{2}\cdot 6761\cdot 81019273^{2} \)	20T1110	Trivial (GRH)
20.12.346253474022222298149289984.1	x^20 - 12x^18 + 63x^16 - 179x^14 + 278x^12 - 205x^10 + 27x^8 + 29x^6 + 6x^4 - 8x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 47^{2}\cdot 347^{4} \)	20T994	Trivial (GRH)
20.12.357012500000000000000000000.1	x^20 - 10x^18 + 35x^16 - 65x^14 + 115x^12 - 235x^10 + 370x^8 - 415x^6 + 290x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{23}\cdot 13^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)
20.12.369301640628035174640123904.1	x^20 - 6x^19 - 2x^18 + 62x^17 - 34x^16 - 272x^15 + 218x^14 + 626x^13 - 771x^12 - 286x^11 + 812x^10 - 262x^9 - 424x^8 + 446x^7 + 76x^6 - 306x^5 + 88x^4 + 72x^3 - 44x^2 + 4x + 1	\( 2^{30}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.382286008207589204343914496.1	x^20 - 2x^19 - 14x^18 + 46x^17 + 17x^16 - 286x^15 + 274x^14 + 468x^13 - 1028x^12 - 272x^11 + 1318x^10 - 358x^9 - 1127x^8 + 510x^7 + 776x^6 - 88x^5 - 257x^4 - 42x^3 + 26x^2 + 10x + 1	\( 2^{30}\cdot 3^{10}\cdot 1567^{4} \)	20T279	Trivial (GRH)
20.12.390543519512736738731951104.1	x^20 - 4x^18 - 5x^16 + 23x^14 + 7x^12 - 44x^10 - x^8 + 31x^6 - 3x^4 - 5x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 43^{2}\cdot 67^{2} \)	20T751	Trivial (GRH)
20.12.390615042633772247314453125.1	x^20 - x^19 - 8x^18 + 16x^17 + x^16 - 86x^15 + 175x^14 + 169x^13 - 704x^12 + 71x^11 + 1178x^10 - 773x^9 - 770x^8 + 1039x^7 - 86x^6 - 417x^5 + 224x^4 - 7x^3 - 30x^2 + 10x - 1	\( 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.12.392139086823683498913562624.1	x^20 - 5x^18 + 8x^16 - 7x^14 + 10x^12 - 47x^10 + 175x^8 - 261x^6 + 165x^4 - 39x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 38569^{4} \)	20T799	Trivial (GRH)
20.12.397047656661540462827405312.1	x^20 - 6x^19 + 16x^18 - 38x^17 + 39x^16 + 174x^15 - 462x^14 + 4x^13 + 742x^12 - 320x^11 - 110x^10 - 298x^9 - 79x^8 + 782x^7 - 620x^6 - 144x^5 + 551x^4 - 146x^3 - 106x^2 + 18x + 1	\( 2^{30}\cdot 13^{4}\cdot 19\cdot 47\cdot 347^{4} \)	20T992	Trivial (GRH)
20.12.423988229267185465614291561.1	x^20 - x^19 - 19x^18 + 9x^17 + 159x^16 + 7x^15 - 733x^14 - 382x^13 + 1886x^12 + 1875x^11 - 2270x^10 - 3913x^9 - 146x^8 + 3180x^7 + 2873x^6 + 300x^5 - 1549x^4 - 1071x^3 - 220x^2 - 4x + 1	\( 3^{10}\cdot 17^{6}\cdot 4153^{4} \)	20T669	Trivial (GRH)
20.12.455293169564857148863676416.1	x^20 - 10x^18 + 36x^16 - 48x^14 - 16x^12 + 96x^10 - 55x^8 - 36x^6 + 42x^4 - 12x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T279	Trivial (GRH)
20.12.455293169564857148863676416.2	x^20 - 10x^18 + 39x^16 - 72x^14 + 82x^12 - 156x^10 + 337x^8 - 372x^6 + 179x^4 - 30x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T568	Trivial (GRH)
20.12.455293169564857148863676416.3	x^20 - 10x^18 + 46x^16 - 128x^14 + 264x^12 - 464x^10 + 629x^8 - 532x^6 + 232x^4 - 40x^2 + 1	\( 2^{40}\cdot 13^{4}\cdot 347^{4} \)	20T673	Trivial (GRH)
20.12.493724556659941556721025024.1	x^20 - 12x^18 + 64x^16 - 195x^14 + 395x^12 - 605x^10 + 686x^8 - 496x^6 + 195x^4 - 33x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 61^{4}\cdot 397^{4} \)	20T669	Trivial (GRH)
20.12.518869631265206280450473984.1	x^20 - 4x^19 + 20x^17 - 47x^16 + 66x^15 + 15x^14 - 236x^13 + 407x^12 - 470x^11 + 54x^10 + 664x^9 + 209x^8 - 1098x^7 - 349x^6 + 858x^5 + 29x^4 - 160x^3 - 11x^2 + 8x + 1	\( 2^{20}\cdot 11^{18}\cdot 89 \)	20T409	Trivial (GRH)
20.12.572447775008070927479996416.1	x^20 - 13x^18 + 73x^16 - 235x^14 + 481x^12 - 649x^10 + 578x^8 - 335x^6 + 120x^4 - 21x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T263	Trivial (GRH)
20.12.572447775008070927479996416.2	x^20 - 9x^18 + 42x^16 - 149x^14 + 377x^12 - 590x^10 + 543x^8 - 293x^6 + 91x^4 - 15x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T341	Trivial (GRH)
20.12.572447775008070927479996416.3	x^20 - 3x^18 + 12x^16 - 32x^14 - 2x^12 + 70x^10 - 17x^8 - 68x^6 + 49x^4 - 12x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 109^{2} \)	20T341	Trivial (GRH)
20.12.601054799445266025059165593.1	x^20 - 15x^18 - 7x^17 + 90x^16 + 70x^15 - 283x^14 - 261x^13 + 470x^12 + 366x^11 - 373x^10 + 42x^9 + 178x^8 - 404x^7 - 116x^6 + 100x^5 - 55x^4 + 8x^3 + 18x^2 - x - 1	\( 307^{5}\cdot 739^{5} \)	20T1106	Trivial (GRH)
20.12.626072689707529169661853696.1	x^20 - 9x^18 + 19x^16 + 29x^14 - 101x^12 - 52x^10 + 254x^8 - 165x^6 + 31x^4 - 7x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4} \)	20T567	Trivial (GRH)
20.12.626072689707529169661853696.2	x^20 - 7x^18 + 15x^16 - x^14 - 34x^12 + 31x^10 + 18x^8 - 46x^6 + 33x^4 - 10x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4} \)	20T964	Trivial (GRH)
20.12.635400276596182371643949056.1	x^20 - 2x^18 - 10x^16 - 2x^14 + 164x^12 - 358x^10 + 255x^8 - 18x^6 - 30x^4 + 1	\( 2^{40}\cdot 4903^{4} \)	20T673	Trivial (GRH)
20.12.705190398026416240151735929.1	x^20 - x^19 - 3x^18 + 8x^17 - 32x^16 - 25x^15 + 185x^14 + x^13 - 381x^12 + 111x^11 + 282x^10 + 3x^9 + 171x^8 - 385x^7 - 362x^6 + 397x^5 + 177x^4 - 133x^3 - 25x^2 + 13x - 1	\( 11^{16}\cdot 43^{4}\cdot 67^{2} \)	20T263	Trivial (GRH)
20.12.743440706348303704240685056.1	x^20 - 5x^19 + 55x^17 - 145x^16 + 56x^15 + 374x^14 - 646x^13 - 88x^12 + 1224x^11 - 568x^10 - 1182x^9 + 657x^8 + 701x^7 - 242x^6 - 211x^5 + 32x^4 + 13x^3 - 20x^2 - 9x - 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T567	Trivial (GRH)
20.12.743440706348303704240685056.2	x^20 - 5x^19 + 41x^17 - 67x^16 - 72x^15 + 292x^14 - 136x^13 - 435x^12 + 527x^11 + 318x^10 - 801x^9 + 11x^8 + 624x^7 - 250x^6 - 174x^5 + 171x^4 - 21x^3 - 30x^2 + 11x - 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T567	Trivial (GRH)
20.12.743440706348303704240685056.3	x^20 - 5x^18 - 14x^16 + 97x^14 - 84x^12 - 147x^10 + 168x^8 + 37x^6 - 46x^4 - 9x^2 + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.12.743440706348303704240685056.4	x^20 - 5x^19 + 5x^18 + 11x^17 - 23x^16 + 30x^15 - 122x^14 + 264x^13 - 230x^12 - 56x^11 + 516x^10 - 688x^9 - x^8 + 653x^7 - 279x^6 - 193x^5 + 128x^4 + 9x^3 - 23x^2 + x + 1	\( 2^{24}\cdot 83^{4}\cdot 983^{4} \)	20T964	Trivial (GRH)
20.12.772549750986794000244140625.1	x^20 - x^19 - 9x^18 + 19x^17 - 12x^16 - 31x^15 + 93x^14 - 138x^13 + 121x^12 - 8x^11 - 126x^10 + 216x^9 - 151x^8 - 26x^7 + 158x^6 - 93x^5 - 68x^4 + 38x^3 + 16x^2 - 3x - 1	\( 3^{4}\cdot 5^{14}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.12.775035034224228831163950629.1	x^20 - 10x^19 + 30x^18 + 15x^17 - 234x^16 + 240x^15 + 665x^14 - 1205x^13 - 949x^12 + 2665x^11 + 766x^10 - 3440x^9 - 433x^8 + 2761x^7 + 251x^6 - 1320x^5 - 119x^4 + 322x^3 + 21x^2 - 27x + 1	\( 461^{2}\cdot 5783^{4}\cdot 3260669 \)	20T1015	Trivial (GRH)
20.12.823067302269314181883621609.1	x^20 - x^19 - 16x^18 + 22x^17 + 96x^16 - 184x^15 - 293x^14 + 814x^13 + 493x^12 - 2154x^11 - 276x^10 + 3939x^9 - 402x^8 - 5522x^7 - 162x^6 + 4485x^5 + 909x^4 - 1760x^3 - 537x^2 + 262x + 89	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.12.823067302269314181883621609.2	x^20 - 7x^19 + 9x^18 + 30x^17 - 53x^16 - 48x^15 - 52x^14 + 227x^13 + 645x^12 - 780x^11 - 1508x^10 + 1074x^9 + 1740x^8 - 558x^7 - 981x^6 + 92x^5 + 261x^4 + 4x^3 - 29x^2 - x + 1	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.12.823067302269314181883621609.3	x^20 - 10x^19 + 41x^18 - 84x^17 + 71x^16 + 44x^15 - 141x^14 + 13x^13 + 280x^12 - 289x^11 - 199x^10 + 626x^9 - 393x^8 - 235x^7 + 468x^6 - 132x^5 - 134x^4 + 75x^3 + 6x^2 - 8x + 1	\( 11^{18}\cdot 23^{6} \)	20T314	Trivial (GRH)
20.12.1242593181789399040000000000.1	x^20 - 7x^18 + 16x^16 - 12x^14 - 16x^10 + 69x^8 - 88x^6 + 49x^4 - 12x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T638	Trivial (GRH)
20.12.1242593181789399040000000000.2	x^20 - 2x^18 - 5x^16 - 6x^14 + 61x^12 - 117x^10 + 174x^8 - 196x^6 + 113x^4 - 25x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T638	Trivial (GRH)