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 160)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.3005062425866291482984448.1	x^20 - 7x^18 + 20x^16 - 26x^14 + 9x^12 + 9x^10 + 2x^8 - 12x^6 + 8	\( 2^{27}\cdot 13^{12}\cdot 31^{2} \)	20T946	Trivial
20.2.10513027966454185188130816.1	x^20 - 3x^18 - 4x^16 + 10x^14 + 5x^12 - 35x^10 + 30x^8 - 8x^6 - 28x^4 + 20x^2 - 4	\( -\,2^{28}\cdot 13^{12}\cdot 41^{2} \)	20T946	Trivial (GRH)
20.2.13634083143995271415857152.1	x^20 - 6x^19 + 16x^18 - 32x^17 + 61x^16 - 112x^15 + 160x^14 - 204x^13 + 274x^12 - 318x^11 + 288x^10 - 318x^9 + 274x^8 - 204x^7 + 160x^6 - 112x^5 + 61x^4 - 32x^3 + 16x^2 - 6x + 1	\( -\,2^{22}\cdot 13^{12}\cdot 41^{2}\cdot 83 \)	20T946	Trivial (GRH)
20.0.23596463127561951644745728.1	x^20 - 8x^19 + 32x^18 - 84x^17 + 172x^16 - 332x^15 + 696x^14 - 1508x^13 + 3024x^12 - 5372x^11 + 8494x^10 - 11982x^9 + 14764x^8 - 15288x^7 + 12752x^6 - 8212x^5 + 3890x^4 - 1268x^3 + 256x^2 - 28x + 2	\( 2^{28}\cdot 7^{3}\cdot 11\cdot 13^{12} \)	20T946	Trivial (GRH)
20.0.46158763415212906841636864.1	x^20 - 8x^19 + 33x^18 - 90x^17 + 174x^16 - 236x^15 + 210x^14 - 98x^13 + 15x^12 - 102x^11 + 355x^10 - 520x^9 + 342x^8 + 62x^7 - 302x^6 + 228x^5 - 24x^4 - 68x^3 + 40x^2 - 8x + 4	\( 2^{22}\cdot 13^{12}\cdot 41^{2}\cdot 281 \)	20T946	Trivial (GRH)
20.4.407881719776428021287747584.1	x^20 - 7x^18 + 21x^16 - 38x^14 + 53x^12 - 77x^10 + 119x^8 - 146x^6 + 119x^4 - 55x^2 + 11	\( 2^{28}\cdot 7^{2}\cdot 11^{3}\cdot 13^{12} \)	20T946	Trivial (GRH)
20.0.407881719776428021287747584.1	x^20 + 7x^18 + 21x^16 + 38x^14 + 53x^12 + 77x^10 + 119x^8 + 146x^6 + 119x^4 + 55x^2 + 11	\( 2^{28}\cdot 7^{2}\cdot 11^{3}\cdot 13^{12} \)	20T946	Trivial (GRH)
20.4.1808152241408540960456444013.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 571x^16 - 1304x^15 + 2466x^14 - 3928x^13 + 5312x^12 - 6106x^11 + 5931x^10 - 4801x^9 + 3165x^8 - 1640x^7 + 655x^6 - 234x^5 + 136x^4 - 110x^3 + 47x^2 - 4x - 1	\( 3^{9}\cdot 17^{12}\cdot 23\cdot 109^{2}\cdot 577 \)	20T946	Trivial (GRH)
20.6.38634172259242566324663091200.1	x^20 + 10x^18 + 43x^16 + 104x^14 + 141x^12 + 62x^10 - 95x^8 - 132x^6 - 25x^4 + 38x^2 - 3	\( -\,2^{20}\cdot 3\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.222532832213237182030059405312.1	x^20 - 4x^19 - x^18 + 24x^17 - 44x^16 + 68x^15 - 100x^14 - 94x^13 + 693x^12 - 1342x^11 + 1719x^10 - 1836x^9 + 1026x^8 + 610x^7 - 1256x^6 + 540x^5 + 79x^4 - 42x^3 - 29x^2 + 14x - 2	\( -\,2^{24}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.222532832213237182030059405312.2	x^20 - 2x^19 - 10x^18 + 40x^17 - 24x^16 - 134x^15 + 333x^14 - 100x^13 - 941x^12 + 2098x^11 - 1638x^10 - 842x^9 + 2653x^8 - 1818x^7 + 110x^6 + 354x^5 + 4x^4 - 164x^3 + 83x^2 - 16x + 1	\( -\,2^{24}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.370888053688728636716765675520.1	x^20 - 3x^17 - 28x^16 - 54x^15 + 202x^14 + 357x^13 - 696x^12 - 438x^11 + 132x^10 - 89x^9 + 4164x^8 - 468x^7 - 7960x^6 + 2885x^5 + 274x^4 - 1064x^3 + 7870x^2 - 5407x + 85	\( 2^{24}\cdot 3^{2}\cdot 5\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.618146756147881061194609459200.1	x^20 - 10x^18 + 43x^16 - 104x^14 + 141x^12 - 62x^10 - 95x^8 + 132x^6 - 25x^4 - 38x^2 - 3	\( -\,2^{24}\cdot 3\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.8.890131328852948728120237621248.1	x^20 - 3x^19 - 7x^18 + 3x^17 + 12x^16 + 92x^15 + 54x^14 - 114x^13 + 275x^12 + 177x^11 - 1497x^10 - 2605x^9 - 364x^8 + 4328x^7 + 5514x^6 + 1128x^5 - 2987x^4 - 2991x^3 - 1311x^2 - 279x - 18	\( 2^{26}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.8.890131328852948728120237621248.2	x^20 - 4x^19 - 2x^18 + 36x^17 - 24x^16 - 210x^15 + 330x^14 + 154x^13 - 917x^12 + 1422x^11 - 1392x^10 - 334x^9 + 2364x^8 - 2062x^7 + 1742x^6 - 1396x^5 + 385x^4 + 98x^3 - 48x^2 + 1	\( 2^{26}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.1030244593579801768657682432000.1	x^20 + 4x^18 - 6x^16 - 88x^14 - 193x^12 + 316x^10 + 950x^8 - 40x^6 - 1131x^4 - 660x^2 - 80	\( -\,2^{24}\cdot 5^{3}\cdot 53^{12} \)	20T946	$[2]$ (GRH)
20.10.1030244593579801768657682432000.1	x^20 - 4x^18 - 6x^16 + 88x^14 - 193x^12 - 316x^10 + 950x^8 + 40x^6 - 1131x^4 + 660x^2 - 80	\( -\,2^{24}\cdot 5^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.1186841771803931637493650161664.1	x^20 + 13x^18 + 46x^16 + 5x^14 - 347x^12 - 972x^10 - 1248x^8 - 798x^6 - 207x^4 - 5x^2 - 1	\( -\,2^{28}\cdot 3^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.1186841771803931637493650161664.1	x^20 - 13x^18 + 46x^16 - 5x^14 - 347x^12 + 972x^10 - 1248x^8 + 798x^6 - 207x^4 + 5x^2 - 1	\( -\,2^{28}\cdot 3^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.1186841771803931637493650161664.2	x^20 + 3x^18 + 4x^16 + x^14 - 2x^12 - 79x^10 - 22x^8 + 321x^6 - 328x^4 + 111x^2 - 9	\( -\,2^{28}\cdot 3^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.1186841771803931637493650161664.2	x^20 - 3x^18 + 4x^16 - x^14 - 2x^12 + 79x^10 - 22x^8 - 321x^6 - 328x^4 - 111x^2 - 9	\( -\,2^{28}\cdot 3^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.1582455695738575516658200215552.1	x^20 - 2x^18 - 9x^16 + 12x^14 - 51x^12 - 24x^10 + 507x^8 + 622x^6 + 169x^4 - 28x^2 - 12	\( -\,2^{30}\cdot 3\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.3296782699455365659704583782400.1	x^20 + 22x^18 + 178x^16 + 652x^14 + 759x^12 - 2384x^10 - 10862x^8 - 18922x^6 - 16999x^4 - 7540x^2 - 1296	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.3296782699455365659704583782400.1	x^20 - 22x^18 + 178x^16 - 652x^14 + 759x^12 + 2384x^10 - 10862x^8 + 18922x^6 - 16999x^4 + 7540x^2 - 1296	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.3296782699455365659704583782400.2	x^20 - 16x^18 + 81x^16 - 56x^14 - 680x^12 + 1704x^10 - 847x^8 - 16x^6 - 1995x^4 + 2224x^2 - 256	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.3296782699455365659704583782400.2	x^20 + 2x^18 - 10x^16 + 24x^14 + 150x^12 + 102x^10 - 329x^8 - 708x^6 - 532x^4 - 160x^2 - 16	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.3296782699455365659704583782400.3	x^20 - 2x^18 - 10x^16 - 24x^14 + 150x^12 - 102x^10 - 329x^8 + 708x^6 - 532x^4 + 160x^2 - 16	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.3296782699455365659704583782400.3	x^20 + 16x^18 + 81x^16 + 56x^14 - 680x^12 - 1704x^10 - 847x^8 + 16x^6 - 1995x^4 - 2224x^2 - 256	\( -\,2^{28}\cdot 5^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.3560525315411794912480950484992.4	x^20 - 6x^18 - 25x^16 + 288x^14 - 636x^12 - 854x^10 + 3895x^8 - 1092x^6 - 883x^4 - 2976x^2 - 768	\( -\,2^{28}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.3560525315411794912480950484992.5	x^20 + 6x^18 - 25x^16 - 288x^14 - 636x^12 + 854x^10 + 3895x^8 + 1092x^6 - 883x^4 + 2976x^2 - 768	\( -\,2^{28}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.3560525315411794912480950484992.6	x^20 + 2x^18 - 41x^16 - 76x^14 - 127x^12 + 46x^10 + 2517x^8 + 3708x^6 + 407x^4 - 1854x^2 - 867	\( -\,2^{28}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.4228123812051506458571128700928.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 592x^16 - 1268x^15 + 2022x^14 - 2164x^13 + 752x^12 + 2612x^11 - 6874x^10 + 9768x^9 - 9327x^8 + 5722x^7 - 1187x^6 - 1794x^5 + 2419x^4 - 1610x^3 + 655x^2 - 154x + 16	\( 2^{24}\cdot 3^{3}\cdot 19\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.5934208859019658187468250808320.1	x^20 - 4x^19 + 4x^18 + 30x^17 - 122x^16 + 98x^15 + 446x^14 - 1426x^13 + 820x^12 + 3542x^11 - 7388x^10 + 1286x^9 + 12893x^8 - 14394x^7 - 3744x^6 + 15684x^5 - 6814x^4 - 4912x^3 + 2248x^2 + 120x + 1340	\( 2^{28}\cdot 3^{2}\cdot 5\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.9527702001426006756546247131136.1	x^20 + 2x^18 - 27x^16 - 198x^14 - 680x^12 - 1378x^10 - 1915x^8 - 1814x^6 - 1119x^4 - 380x^2 - 64	\( -\,2^{26}\cdot 17^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.2.9527702001426006756546247131136.2	x^20 - 2x^18 - 27x^16 + 198x^14 - 680x^12 + 1378x^10 - 1915x^8 + 1814x^6 - 1119x^4 + 380x^2 - 64	\( -\,2^{26}\cdot 17^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.14242101261647179649923801939968.1	x^20 - 6x^19 + 23x^18 - 54x^17 + 92x^16 - 80x^15 - 84x^14 + 818x^13 - 2963x^12 + 7528x^11 - 12325x^10 + 9438x^9 + 12388x^8 - 51286x^7 + 85532x^6 - 86716x^5 + 52301x^4 - 7376x^3 - 12029x^2 + 7832x - 2536	\( 2^{30}\cdot 3^{3}\cdot 53^{12} \)	20T946	$[2]$ (GRH)
20.12.14242101261647179649923801939968.1	x^20 - 6x^19 - 3x^18 + 92x^17 - 164x^16 - 372x^15 + 1636x^14 - 844x^13 - 5371x^12 + 9010x^11 + 5133x^10 - 18932x^9 - 2738x^8 + 20648x^7 + 11246x^6 - 23868x^5 - 12104x^4 + 19712x^3 + 564x^2 - 4320x + 872	\( 2^{30}\cdot 3^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.14315153843200000000000000000000.1	x^20 - 5x^18 - 10x^17 - 120x^16 - 110x^15 - 710x^14 - 550x^13 - 2055x^12 - 1630x^11 - 2869x^10 - 2570x^9 - 1100x^8 - 1720x^7 + 1070x^6 - 38x^5 + 410x^4 - 140x^3 + 10x^2 - 20x + 6	\( 2^{28}\cdot 5^{20}\cdot 7^{8}\cdot 97 \)	20T946	Trivial (GRH)
20.8.14315153843200000000000000000000.1	x^20 - 20x^18 - 30x^17 + 205x^16 + 412x^15 - 1010x^14 - 2160x^13 + 1940x^12 + 4900x^11 - 1690x^10 - 4200x^9 + 6100x^8 + 6600x^7 - 9050x^6 - 13300x^5 - 2125x^4 + 4000x^3 + 2250x^2 + 250x - 125	\( 2^{28}\cdot 5^{20}\cdot 7^{8}\cdot 97 \)	20T946	Trivial (GRH)
20.4.14315153843200000000000000000000.2	x^20 - 5x^18 - 10x^17 + 55x^16 + 28x^15 - 150x^14 - 20x^13 + 105x^12 + 240x^11 + 801x^10 - 1490x^9 - 275x^8 - 360x^7 + 590x^6 + 1904x^5 - 1505x^4 - 100x^3 + 455x^2 - 270x + 45	\( 2^{28}\cdot 5^{20}\cdot 7^{8}\cdot 97 \)	20T946	Trivial (GRH)
20.14.21696405043600000000000000000000.1	x^20 - 25x^18 + 190x^16 - 410x^14 + 105x^12 + 439x^10 - 260x^8 - 100x^6 + 80x^4 - 4	\( -\,2^{22}\cdot 5^{20}\cdot 7^{8}\cdot 97^{2} \)	20T946	Trivial (GRH)
20.6.21696405043600000000000000000000.1	x^20 - 5x^19 + 55x^17 - 140x^16 + 23x^15 + 360x^14 - 285x^13 - 215x^12 - 1610x^11 + 4630x^10 + 2110x^9 - 16815x^8 + 10795x^7 + 22820x^6 - 44429x^5 + 30310x^4 + 805x^3 - 21670x^2 + 18225x - 4721	\( -\,2^{22}\cdot 5^{20}\cdot 7^{8}\cdot 97^{2} \)	20T946	Trivial (GRH)
20.10.21696405043600000000000000000000.2	x^20 - 5x^18 - 20x^17 - 60x^16 + 56x^15 + 430x^14 + 260x^13 + 175x^12 + 800x^11 + 1063x^10 - 2710x^9 - 3290x^8 + 100x^7 + 2240x^6 + 2182x^5 - 820x^4 - 840x^3 + 220x^2 + 20x - 2	\( -\,2^{22}\cdot 5^{20}\cdot 7^{8}\cdot 97^{2} \)	20T946	Trivial (GRH)
20.6.25319291131817208266531203448832.1	x^20 + 4x^18 - 46x^16 + 208x^14 + 915x^12 - 8544x^10 + 3342x^8 + 21460x^6 + 12017x^4 + 1120x^2 - 108	\( -\,2^{34}\cdot 3\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.25319291131817208266531203448832.1	x^20 - 12x^18 - 28x^17 + 146x^16 + 188x^15 - 1272x^14 + 728x^13 + 3982x^12 - 5796x^11 - 4320x^10 + 11304x^9 + 1816x^8 - 11136x^7 - 456x^6 + 6192x^5 - 1788x^4 - 936x^3 + 640x^2 - 128x + 8	\( -\,2^{34}\cdot 3\cdot 53^{12} \)	20T946	Trivial (GRH)
20.4.26627057862792569136621049085952.1	x^20 - 2x^19 + 3x^18 - 44x^17 + 103x^16 - 82x^15 + 38x^14 + 566x^13 - 1128x^12 - 468x^11 + 773x^10 + 1954x^9 - 7191x^8 + 22962x^7 - 29020x^6 - 11274x^5 + 51246x^4 - 35544x^3 + 5377x^2 + 2216x - 768	\( 2^{18}\cdot 3\cdot 41^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.8.26627057862792569136621049085952.1	x^20 - 3x^19 - 5x^18 - 4x^17 - 18x^16 + 92x^15 + 194x^14 + 264x^13 + 266x^12 - 298x^11 - 743x^10 - 905x^9 + 359x^8 + 1866x^7 - 1585x^6 - 575x^5 + 2093x^4 - 1304x^3 + 335x^2 - 35x + 1	\( 2^{18}\cdot 3\cdot 41^{3}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.6.47605542180135480126134189817856.1	x^20 + 15x^18 + 67x^16 + 62x^14 - 172x^12 - 36x^10 + 723x^8 + 233x^6 - 366x^4 + 73x^2 - 1	\( -\,2^{28}\cdot 19^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.47605542180135480126134189817856.1	x^20 - 11x^18 - x^16 + 408x^14 - 1570x^12 + 1514x^10 + 898x^8 - 1200x^6 + 161x^4 + 57x^2 - 1	\( -\,2^{28}\cdot 19^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)
20.10.47605542180135480126134189817856.2	x^20 - 15x^18 + 67x^16 - 62x^14 - 172x^12 + 36x^10 + 723x^8 - 233x^6 - 366x^4 - 73x^2 - 1	\( -\,2^{28}\cdot 19^{2}\cdot 53^{12} \)	20T946	Trivial (GRH)