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 76)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.541040645705284358852575232.1	x^20 - 10x^18 + 49x^16 - 152x^14 + 304x^12 - 368x^10 + 249x^8 - 100x^6 + 76x^4 - 80x^2 + 32	\( 2^{37}\cdot 89^{8} \)	20T803	Trivial (GRH)
20.0.541040645705284358852575232.2	x^20 - 2x^18 + 3x^16 - 14x^14 + 21x^12 + 14x^10 - 46x^8 + 10x^6 + 29x^4 - 14x^2 + 2	\( 2^{37}\cdot 89^{8} \)	20T803	Trivial (GRH)
20.2.634749729177600000000000000.2	x^20 + 5x^18 + x^16 - 26x^14 - 19x^12 + 55x^10 + 55x^8 - 22x^6 + 7x^4 + 33x^2 - 9	\( -\,2^{28}\cdot 3^{18}\cdot 5^{14} \)	20T803	Trivial (GRH)
20.2.634749729177600000000000000.3	x^20 - 5x^18 + x^16 + 26x^14 - 19x^12 - 55x^10 + 55x^8 + 22x^6 + 7x^4 - 33x^2 - 9	\( -\,2^{28}\cdot 3^{18}\cdot 5^{14} \)	20T803	Trivial (GRH)
20.0.1439177057495117187500000000.1	x^20 + 5x^12 + 33x^10 + 75x^8 + 115x^6 + 110x^4 + 55x^2 + 11	\( 2^{8}\cdot 5^{22}\cdot 11^{9} \)	20T803	Trivial (GRH)
20.4.1983468096640110015869140625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 105x^16 + 228x^15 + 90x^14 - 540x^13 + 50x^12 + 740x^11 - 53x^10 - 885x^9 + 135x^8 + 540x^7 + 65x^6 - 306x^5 - 25x^4 + 65x^3 + 10x^2 - 5x - 1	\( 5^{22}\cdot 11^{8}\cdot 3881 \)	20T803	Trivial (GRH)
20.0.2919444013905417972500000000.1	x^20 + 14x^18 + 83x^16 + 272x^14 + 542x^12 + 697x^10 + 667x^8 + 668x^6 + 713x^4 + 505x^2 + 149	\( 2^{8}\cdot 5^{10}\cdot 97^{8}\cdot 149 \)	20T803	Trivial (GRH)
20.4.106492446508915367663587954688.1	x^20 - 8x^18 - 3x^16 + 16x^14 - 66x^12 + 114x^10 + 324x^8 + 38x^6 + 870x^4 + 377	\( 2^{12}\cdot 13^{11}\cdot 29^{9} \)	20T803	Trivial (GRH)
20.12.30600403651756787034535404044288.1	x^20 - 10x^19 + 27x^18 + 42x^17 - 426x^16 + 1164x^15 - 1564x^14 + 370x^13 + 2505x^12 - 4448x^11 + 2667x^10 + 1564x^9 - 3856x^8 + 2254x^7 + 402x^6 - 1092x^5 + 372x^4 + 108x^3 - 84x^2 + 4x + 4	\( 2^{16}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.397805247472838231448960252575744.1	x^20 - 10x^19 + 40x^18 - 75x^17 + 15x^16 + 288x^15 - 740x^14 + 650x^13 + 686x^12 - 2556x^11 + 2638x^10 + 620x^9 - 4329x^8 + 3660x^7 + 546x^6 - 3173x^5 + 1828x^4 + 466x^3 - 698x^2 + 143x + 13	\( 2^{16}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.8.397805247472838231448960252575744.1	x^20 - 7x^19 - x^18 + 89x^17 - 52x^16 - 519x^15 + 117x^14 + 1945x^13 + 1264x^12 - 6435x^11 + 1105x^10 - 3575x^9 - 9126x^8 + 64675x^7 - 79677x^6 + 96317x^5 + 1378x^4 - 245479x^3 + 41795x^2 + 165945x - 6877	\( 2^{16}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.397805247472838231448960252575744.2	x^20 - 9x^19 + 17x^18 + 81x^17 - 360x^16 + 5x^15 + 2099x^14 - 1973x^13 - 5862x^12 + 6877x^11 + 9551x^10 - 7985x^9 - 8322x^8 + 2115x^7 - 2731x^6 - 6223x^5 + 14836x^4 + 11897x^3 - 8527x^2 - 1677x + 793	\( 2^{16}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.489606458428108592552566464708608.1	x^20 - 8x^19 + 9x^18 + 88x^17 - 291x^16 + 52x^15 + 990x^14 - 1138x^13 - 1279x^12 + 3424x^11 - 791x^10 - 5110x^9 + 5625x^8 + 2028x^7 - 5876x^6 + 962x^5 + 1677x^4 + 130x^3 - 325x^2 - 338x + 169	\( 2^{20}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.8.489606458428108592552566464708608.1	x^20 - 4x^19 - 5x^18 + 26x^17 + 7x^16 + 86x^15 - 148x^14 - 1462x^13 + 1035x^12 + 7250x^11 - 1905x^10 - 20880x^9 - 2467x^8 + 39476x^7 + 18342x^6 - 45500x^5 - 42341x^4 + 7332x^3 + 19227x^2 + 5122x - 299	\( 2^{20}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.8.489606458428108592552566464708608.2	x^20 - 4x^19 - 8x^18 + 96x^17 - 336x^16 + 706x^15 - 1286x^14 + 3224x^13 - 8972x^12 + 21568x^11 - 44968x^10 + 79288x^9 - 112192x^8 + 121188x^7 - 87016x^6 + 20424x^5 + 29868x^4 - 33056x^3 + 12252x^2 - 104x - 452	\( 2^{20}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.10.4360118487671115706531840000000000.3	x^20 + 5x^18 - 73x^16 + 88x^14 + 422x^12 - 642x^10 - 718x^8 + 1144x^6 + 329x^4 - 515x^2 - 25	\( -\,2^{40}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.10.4360118487671115706531840000000000.4	x^20 - 5x^18 - 73x^16 - 88x^14 + 422x^12 + 642x^10 - 718x^8 - 1144x^6 + 329x^4 + 515x^2 - 25	\( -\,2^{40}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.8.5171468217146897008836483283484672.1	x^20 - 4x^19 - 2x^18 - 20x^17 + 91x^16 + 106x^15 + 210x^14 - 274x^13 - 628x^12 - 4614x^11 - 11190x^10 - 2786x^9 + 21516x^8 + 43966x^7 + 92334x^6 + 210906x^5 + 270099x^4 + 150562x^3 + 17272x^2 - 8466x - 391	\( 2^{16}\cdot 13^{16}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.8.5171468217146897008836483283484672.2	x^20 - 2x^19 - 17x^18 + 14x^17 + 189x^16 - 64x^15 - 1444x^14 + 336x^13 + 5827x^12 + 554x^11 - 8641x^10 + 2940x^9 - 1065x^8 + 4264x^7 + 11828x^6 - 11602x^5 - 5705x^4 + 2250x^3 - 3297x^2 + 1248x + 1733	\( 2^{16}\cdot 13^{16}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.6364883959565411703183364041211904.1	x^20 - 4x^19 - 30x^18 + 120x^17 + 329x^16 - 1348x^15 - 1662x^14 + 7344x^13 + 3922x^12 - 20634x^11 - 2990x^10 + 25938x^9 - 2738x^8 + 4652x^7 + 4914x^6 - 51880x^5 - 8279x^4 + 49930x^3 + 14300x^2 - 8430x - 2323	\( 2^{20}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.4.6364883959565411703183364041211904.1	x^20 - 10x^19 + 51x^18 - 154x^17 + 241x^16 - 56x^15 - 484x^14 + 30x^13 + 2929x^12 - 3012x^11 - 7085x^10 + 17914x^9 + 31517x^8 - 62418x^7 - 179044x^6 + 35680x^5 + 388589x^4 + 412952x^3 - 199529x^2 - 519520x - 453883	\( 2^{20}\cdot 13^{15}\cdot 17^{9} \)	20T803	$[2]$ (GRH)
20.8.6364883959565411703183364041211904.1	x^20 - 4x^19 - 11x^18 + 48x^17 - 11x^16 + 260x^15 - 1426x^14 + 2382x^13 - 4213x^12 + 12906x^11 - 25957x^10 + 33292x^9 - 43527x^8 + 74738x^7 - 101662x^6 + 72180x^5 - 4859x^4 - 27164x^3 + 14947x^2 - 1464x - 439	\( 2^{20}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.6364883959565411703183364041211904.2	x^20 - 8x^19 + 12x^18 + 40x^17 - 54x^16 - 148x^15 - 478x^14 + 1392x^13 + 2246x^12 + 4108x^11 - 32760x^10 + 11700x^9 + 35984x^8 + 58708x^7 - 90012x^6 - 111956x^5 + 125736x^4 + 34060x^3 - 40560x^2 + 5928x - 52	\( 2^{20}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.6364883959565411703183364041211904.3	x^20 - 4x^19 - 17x^18 + 98x^17 - 39x^16 - 614x^15 + 1376x^14 + 448x^13 - 6317x^12 + 7738x^11 + 8537x^10 - 29184x^9 + 9753x^8 + 43582x^7 - 38038x^6 - 28416x^5 + 36271x^4 + 5396x^3 - 12923x^2 + 392x + 1439	\( 2^{20}\cdot 13^{15}\cdot 17^{9} \)	20T803	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)
20.2.7372897256329164687850412645023744.1	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)
20.10.7372897256329164687850412645023744.4	x^20 - 24x^18 - 9x^16 + 180x^14 + 66x^12 - 368x^10 - 94x^8 + 260x^6 + 21x^4 - 48x^2 - 1	\( -\,2^{28}\cdot 13^{14}\cdot 17^{8} \)	20T803	Trivial (GRH)
20.10.7372897256329164687850412645023744.5	x^20 + 24x^18 - 9x^16 - 180x^14 + 66x^12 + 368x^10 - 94x^8 - 260x^6 + 21x^4 + 48x^2 - 1	\( -\,2^{28}\cdot 13^{14}\cdot 17^{8} \)	20T803	Trivial (GRH)
20.12.7833703334849737480841063435337728.1	x^20 - 6x^18 - 23x^16 + 116x^14 + 90x^12 - 596x^10 + 94x^8 + 852x^6 - 323x^4 - 238x^2 + 17	\( 2^{24}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.16.7833703334849737480841063435337728.1	x^20 - 28x^18 + 188x^16 + 172x^14 - 6496x^12 + 27828x^10 - 52784x^8 + 48096x^6 - 19040x^4 + 1904x^2 + 272	\( 2^{24}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.4.7833703334849737480841063435337728.1	x^20 + 25x^18 + 219x^16 + 630x^14 - 1991x^12 - 19365x^10 - 55379x^8 - 68790x^6 - 22389x^4 + 19805x^2 + 8993	\( 2^{24}\cdot 13^{14}\cdot 17^{9} \)	20T803	$[4]$ (GRH)
20.8.7833703334849737480841063435337728.1	x^20 + 9x^18 - 129x^16 - 562x^14 + 4881x^12 + 1151x^10 - 11291x^8 - 5722x^6 + 1751x^4 + 901x^2 + 17	\( 2^{24}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.12.7833703334849737480841063435337728.2	x^20 - 4x^19 + 2x^18 + 100x^17 - 180x^16 - 604x^15 + 476x^14 + 2116x^13 + 572x^12 - 2624x^11 - 2052x^10 - 1864x^9 - 3728x^8 - 1072x^7 + 12560x^6 + 10576x^5 - 3872x^4 - 4208x^3 + 160x^2 + 320x - 16	\( 2^{24}\cdot 13^{14}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.14.21800592438355578532659200000000000.1	x^20 - 21x^18 - 22x^17 + 31x^16 + 688x^15 + 1554x^14 - 7300x^13 - 11818x^12 + 34332x^11 + 41076x^10 - 80412x^9 - 103678x^8 + 125000x^7 + 174218x^6 - 170940x^5 - 121595x^4 + 132356x^3 + 5801x^2 - 18814x - 461	\( -\,2^{40}\cdot 5^{11}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.6.21800592438355578532659200000000000.1	x^20 - 2x^19 - 22x^18 + 66x^17 + 39x^16 - 84x^15 - 300x^14 - 2076x^13 + 7976x^12 - 5260x^11 - 5116x^10 + 3436x^9 - 632x^8 + 43380x^7 - 28732x^6 - 19220x^5 + 15491x^4 - 5370x^3 + 13378x^2 - 9222x + 2269	\( -\,2^{40}\cdot 5^{11}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.14.21800592438355578532659200000000000.2	x^20 - 2x^19 - 22x^18 + 12x^17 + 228x^16 + 152x^15 - 1080x^14 - 1780x^13 + 1733x^12 + 5846x^11 - 582x^10 - 8844x^9 + 6580x^8 + 17908x^7 - 10376x^6 - 19316x^5 + 7075x^4 + 7366x^3 - 2794x^2 - 424x + 164	\( -\,2^{40}\cdot 5^{11}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.6.21800592438355578532659200000000000.2	x^20 - 4x^19 + 6x^18 + 12x^17 - 158x^16 + 600x^15 - 1764x^14 + 4176x^13 - 3001x^12 - 20296x^11 + 92638x^10 - 210004x^9 + 296708x^8 - 275856x^7 + 181220x^6 - 110860x^5 + 104855x^4 - 108140x^3 + 72506x^2 - 28260x + 4276	\( -\,2^{40}\cdot 5^{11}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.14.69761895802737851304509440000000000.1	x^20 - 12x^18 - 129x^16 + 1736x^14 + 542x^12 - 28592x^10 - 11822x^8 + 24504x^6 - 3951x^4 + 124x^2 - 1	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.6.69761895802737851304509440000000000.1	x^20 + 12x^18 - 129x^16 - 1736x^14 + 542x^12 + 28592x^10 - 11822x^8 - 24504x^6 - 3951x^4 - 124x^2 - 1	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.10.69761895802737851304509440000000000.2	x^20 - 126x^16 - 88x^14 + 2747x^12 + 3988x^10 - 4638x^8 - 804x^6 + 705x^4 + 76x^2 - 16	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.14.69761895802737851304509440000000000.2	x^20 - 15x^18 - 103x^16 + 954x^14 + 2017x^12 - 3645x^10 - 2285x^8 + 5318x^6 - 2429x^4 + 313x^2 - 1	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.6.69761895802737851304509440000000000.2	x^20 + 15x^18 - 103x^16 - 954x^14 + 2017x^12 + 3645x^10 - 2285x^8 - 5318x^6 - 2429x^4 - 313x^2 - 1	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.10.69761895802737851304509440000000000.3	x^20 - 126x^16 + 88x^14 + 2747x^12 - 3988x^10 - 4638x^8 + 804x^6 + 705x^4 - 76x^2 - 16	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.14.69761895802737851304509440000000000.3	x^20 - 98x^16 + 560x^14 - 977x^12 - 276x^10 + 2282x^8 - 1796x^6 + 241x^4 + 84x^2 - 16	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.6.69761895802737851304509440000000000.3	x^20 - 98x^16 - 560x^14 - 977x^12 + 276x^10 + 2282x^8 + 1796x^6 + 241x^4 - 84x^2 - 16	\( -\,2^{44}\cdot 5^{10}\cdot 67^{8} \)	20T803	Trivial (GRH)
20.16.82743491474350352141383732535754752.1	x^20 - 4x^19 - 27x^18 + 124x^17 + 205x^16 - 1270x^15 - 352x^14 + 5810x^13 - 2155x^12 - 12082x^11 + 12289x^10 + 4578x^9 - 22931x^8 + 19318x^7 + 15716x^6 - 23726x^5 - 3927x^4 + 9548x^3 + 127x^2 - 1274x + 49	\( 2^{20}\cdot 13^{16}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.8.82743491474350352141383732535754752.1	x^20 + 17x^18 - 113x^16 - 1950x^14 + 481x^12 + 37063x^10 + 34697x^8 - 82030x^6 - 75361x^4 - 8619x^2 + 2873	\( 2^{20}\cdot 13^{16}\cdot 17^{9} \)	20T803	Trivial (GRH)
20.14.95847664332279140942055364385308672.1	x^20 - 10x^19 + 36x^18 - 26x^17 - 303x^16 + 1262x^15 - 1246x^14 - 3770x^13 + 15238x^12 - 20006x^11 - 33804x^10 + 118742x^9 - 19932x^8 - 195946x^7 + 138490x^6 + 85254x^5 - 120159x^4 + 33124x^3 + 5096x^2 - 3224x + 299	\( -\,2^{28}\cdot 13^{15}\cdot 17^{8} \)	20T803	Trivial (GRH)
20.6.95847664332279140942055364385308672.1	x^20 + 21x^18 - 15x^16 - 1102x^14 - 3347x^12 + 559x^10 + 10099x^8 + 5098x^6 - 5253x^4 - 1651x^2 - 13	\( -\,2^{28}\cdot 13^{15}\cdot 17^{8} \)	20T803	Trivial (GRH)
20.12.101838143353046587250933824659390464.1	x^20 - 4x^19 - 14x^18 + 8x^17 + 141x^16 + 586x^15 - 828x^14 - 1822x^13 - 6400x^12 + 1606x^11 + 20388x^10 - 16634x^9 + 29636x^8 + 610x^7 - 56540x^6 + 4434x^5 + 20511x^4 + 4898x^3 + 126x^2 - 26x - 1	\( 2^{24}\cdot 13^{15}\cdot 17^{9} \)	20T803	Trivial (GRH)