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 74)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.322809648674379833984375.1	x^20 - 2x^19 + 4x^18 - 15x^17 + 28x^16 - 32x^15 + 57x^14 - 95x^13 + 89x^12 - 90x^11 + 119x^10 - 92x^9 + 57x^8 - 60x^7 + 36x^6 + 4x^5 - 2x^4 + 2x^3 - 10x^2 + 5x + 1	\( -\,5^{11}\cdot 1459^{5} \)	20T1023	Trivial (GRH)
20.0.752023303669760000000000.1	x^20 - 2x^19 + 3x^18 - 2x^17 + 3x^16 + 18x^14 - 34x^13 + 77x^12 - 98x^11 + 139x^10 - 140x^9 + 151x^8 - 124x^7 + 92x^6 - 70x^5 + 35x^4 - 22x^3 + 11x^2 + 2x + 1	\( 2^{20}\cdot 5^{10}\cdot 149^{5} \)	20T1023	Trivial (GRH)
20.2.1292066884157440000000000.3	x^20 + 3x^18 + 13x^16 + 26x^14 + 33x^12 + 49x^10 + 55x^8 + 26x^6 - x^4 - 5x^2 - 1	\( -\,2^{28}\cdot 5^{10}\cdot 149^{4} \)	20T1023	Trivial (GRH)
20.0.1333793751314223595520000.1	x^20 - 2x^18 + 4x^16 - 4x^14 + 17x^12 - 34x^10 + 62x^8 - 64x^6 + 52x^4 - 24x^2 + 8	\( 2^{37}\cdot 5^{4}\cdot 353^{4} \)	20T1023	Trivial (GRH)
20.0.2676960704021115830230512.1	x^20 - 9x^19 + 42x^18 - 135x^17 + 322x^16 - 563x^15 + 685x^14 - 484x^13 - 76x^12 + 770x^11 - 1177x^10 + 996x^9 - 365x^8 - 306x^7 + 697x^6 - 721x^5 + 518x^4 - 274x^3 + 109x^2 - 30x + 4	\( 2^{4}\cdot 3^{10}\cdot 4903^{5} \)	20T1023	Trivial (GRH)
20.4.34911277180920342783203125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 569x^16 - 1288x^15 + 2401x^14 - 3753x^13 + 4971x^12 - 5607x^11 + 5381x^10 - 4361x^9 + 2928x^8 - 1561x^7 + 585x^6 - 74x^5 - 93x^4 + 89x^3 - 44x^2 + 13x - 1	\( 5^{10}\cdot 1459^{4}\cdot 788941 \)	20T1023	Trivial (GRH)
20.4.192517965739458560000000000.1	x^20 + 11x^18 + 59x^16 + 202x^14 + 501x^12 + 941x^10 + 1289x^8 + 950x^6 - 149x^4 - 745x^2 + 149	\( 2^{28}\cdot 5^{10}\cdot 149^{5} \)	20T1023	Trivial (GRH)
20.0.836446705572425050830078125.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1055x^16 - 3136x^15 + 7913x^14 - 17137x^13 + 32320x^12 - 53273x^11 + 77195x^10 - 98188x^9 + 109636x^8 - 106721x^7 + 90006x^6 - 64742x^5 + 39041x^4 - 19036x^3 + 7146x^2 - 1843x + 251	\( 5^{11}\cdot 31\cdot 1459^{4}\cdot 121951 \)	20T1023	Trivial (GRH)
20.6.59313783170950766384309600256.1	x^20 - 6x^19 + 21x^18 - 24x^17 - 15x^16 + 162x^15 - 217x^14 - 12x^13 + 447x^12 - 600x^11 - 294x^10 + 744x^9 + 463x^8 - 78x^7 - 753x^6 - 342x^5 + 471x^4 + 216x^3 - 108x^2 - 36x + 9	\( -\,2^{20}\cdot 3^{19}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.6.59313783170950766384309600256.2	x^20 - 4x^19 + 10x^18 - 2x^17 - 22x^16 + 40x^15 - 52x^14 + 118x^13 - 121x^12 - 254x^11 + 509x^10 - 104x^9 - 838x^8 + 1036x^7 + 374x^6 - 1490x^5 + 230x^4 + 850x^3 - 119x^2 - 166x - 23	\( -\,2^{20}\cdot 3^{19}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.6.59313783170950766384309600256.3	x^20 - 2x^19 - 2x^18 - 10x^17 + 23x^16 - 28x^15 + 23x^14 + 32x^13 - 22x^12 + 38x^11 - 25x^10 + 38x^9 - 22x^8 + 32x^7 + 23x^6 - 28x^5 + 23x^4 - 10x^3 - 2x^2 - 2x + 1	\( -\,2^{20}\cdot 3^{19}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.6.59313783170950766384309600256.4	x^20 - 4x^19 + 10x^18 - 8x^17 - 16x^16 + 46x^15 - 82x^14 + 106x^13 - 58x^12 - 218x^11 + 845x^10 - 980x^9 - 766x^8 + 2974x^7 - 1357x^6 - 2888x^5 + 2825x^4 + 970x^3 - 1826x^2 + 2x + 433	\( -\,2^{20}\cdot 3^{19}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.2.357867026381710908800000000000.1	x^20 - 5x^19 + 25x^18 - 80x^17 + 219x^16 - 497x^15 + 891x^14 - 1376x^13 + 1783x^12 - 1335x^11 + 2183x^10 + 722x^9 + 3158x^8 + 816x^7 + 642x^6 + 1010x^5 + 2092x^4 + 2248x^3 + 1084x^2 + 240x + 20	\( -\,2^{16}\cdot 5^{11}\cdot 19^{5}\cdot 461^{4} \)	20T1023	Trivial (GRH)
20.10.1145174484421474908160000000000.1	x^20 - 20x^18 + 156x^16 - 620x^14 + 1304x^12 - 1212x^10 - 320x^8 + 2064x^6 - 2560x^4 + 1520x^2 - 304	\( -\,2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 461^{4} \)	20T1023	Trivial (GRH)
20.10.2115524933097244001040375742464.1	x^20 - 6x^19 + x^18 + 68x^17 - 153x^16 - 106x^15 + 882x^14 - 1332x^13 + 543x^12 + 1200x^11 - 4068x^10 + 8490x^9 - 10887x^8 + 6180x^7 + 3300x^6 - 9272x^5 + 8319x^4 - 4256x^3 + 1294x^2 - 210x + 13	\( -\,2^{20}\cdot 3^{18}\cdot 13^{5}\cdot 107^{5} \)	20T1023	Trivial (GRH)
20.2.2115524933097244001040375742464.1	x^20 - 7x^18 - 16x^17 + 18x^16 + 100x^15 + 102x^14 - 222x^13 - 93x^12 + 1168x^11 + 15x^10 - 814x^9 + 791x^8 - 636x^7 + 2038x^6 - 384x^5 - 2151x^4 + 2040x^3 - 3366x^2 + 252x - 423	\( -\,2^{20}\cdot 3^{18}\cdot 13^{5}\cdot 107^{5} \)	20T1023	Trivial (GRH)
20.8.8682984166419406787200000000000.1	x^20 - 3x^19 + 6x^18 + 17x^17 - 54x^16 + 35x^15 + 12x^14 - 529x^13 - 525x^12 - 718x^11 - 2276x^10 - 2612x^9 - 991x^8 - 461x^7 + 1294x^6 + 4241x^5 + 1708x^4 - 2021x^3 - 820x^2 + 311x + 29	\( 2^{16}\cdot 5^{11}\cdot 19^{4}\cdot 461^{5} \)	20T1023	Trivial (GRH)
20.10.10024029355890679518948322443264.2	x^20 - 6x^19 + 3x^18 + 22x^17 - 15x^16 + 30x^15 + 81x^14 - 330x^13 - 300x^12 + 190x^11 - 315x^10 + 156x^9 + 637x^8 - 1302x^7 - 1782x^6 - 210x^5 + 498x^4 + 306x^3 + 48x^2 - 12x - 3	\( -\,2^{20}\cdot 3^{19}\cdot 13^{7}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.2.18322791750743598530560000000000.1	x^20 + 17x^18 + 59x^16 + 218x^14 + 2037x^12 + 4399x^10 + 2117x^8 - 2198x^6 - 2681x^4 - 931x^2 - 19	\( -\,2^{24}\cdot 5^{10}\cdot 19^{5}\cdot 461^{4} \)	20T1023	$[2]$ (GRH)
20.4.20245771322351194925844343554048.1	x^20 - 10x^19 + 48x^18 - 126x^17 + 129x^16 + 324x^15 - 1720x^14 + 4120x^13 - 6993x^12 + 9562x^11 - 10414x^10 + 7344x^9 - 849x^8 - 4512x^7 + 6732x^6 - 7270x^5 + 3280x^4 + 4644x^3 - 5310x^2 + 876x - 183	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.8.20245771322351194925844343554048.1	x^20 - 4x^19 - 14x^18 + 98x^17 - 107x^16 - 412x^15 + 1464x^14 - 1632x^13 - 999x^12 + 5974x^11 - 9004x^10 + 5944x^9 + 87x^8 - 2208x^7 + 552x^6 + 140x^5 - 134x^4 + 56x^3 + 16x^2 - 10x + 1	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.4.20245771322351194925844343554048.2	x^20 - 4x^18 - 30x^16 + 74x^14 - 113x^12 + 1104x^10 - 1989x^8 - 2664x^6 + 5427x^4 + 5670x^2 + 1053	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.8.20245771322351194925844343554048.2	x^20 - 8x^19 + 12x^18 + 56x^17 - 208x^16 + 186x^15 + 86x^14 - 40x^13 - 567x^12 + 1510x^11 - 1976x^10 + 552x^9 + 642x^8 + 2580x^7 - 7410x^6 - 126x^5 + 846x^4 + 8388x^3 + 5616x^2 - 351	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.4.20245771322351194925844343554048.3	x^20 - 8x^19 + 38x^18 - 130x^17 + 314x^16 - 500x^15 + 432x^14 + 234x^13 - 1827x^12 + 3600x^11 - 2772x^10 - 2364x^9 + 9758x^8 - 15790x^7 + 15058x^6 - 5460x^5 - 5568x^4 + 9300x^3 - 6124x^2 + 2012x - 263	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.8.20245771322351194925844343554048.3	x^20 - 10x^19 + 28x^18 + 18x^17 - 207x^16 + 192x^15 + 584x^14 - 1154x^13 - 616x^12 + 3232x^11 - 1624x^10 - 3584x^9 + 4489x^8 + 1268x^7 - 5930x^6 + 3982x^5 + 419x^4 - 2114x^3 + 1240x^2 - 274x + 13	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.4.20245771322351194925844343554048.4	x^20 - 10x^19 + 52x^18 - 168x^17 + 330x^16 - 408x^15 + 544x^14 - 1342x^13 + 2788x^12 - 3600x^11 + 3180x^10 - 3042x^9 + 4891x^8 - 7612x^7 + 8050x^6 - 5412x^5 + 2700x^4 - 1176x^3 + 774x^2 - 540x + 117	\( 2^{30}\cdot 3^{18}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.2.32995339832393745791360000000000.1	x^20 - x^19 - 9x^18 + 10x^17 + 35x^16 + 93x^15 - 299x^14 - 328x^13 + 1499x^12 - 1781x^11 + 3689x^10 - 7018x^9 + 8662x^8 - 5178x^7 - 5938x^6 + 33062x^5 - 60328x^4 + 65700x^3 - 42116x^2 + 22672x - 8156	\( -\,2^{16}\cdot 5^{10}\cdot 19^{5}\cdot 461^{5} \)	20T1023	Trivial (GRH)
20.10.47806331471833622563812255859375.1	x^20 - 5x^19 - 3x^18 + 27x^17 + 23x^16 + 68x^15 - 297x^14 - 965x^13 + 1109x^12 + 2960x^11 - 763x^10 - 2284x^9 - 5131x^8 - 2908x^7 + 15301x^6 + 2854x^5 - 14062x^4 - 804x^3 + 3870x^2 + 79x - 31	\( -\,5^{15}\cdot 11^{5}\cdot 9931^{4} \)	20T1023	Trivial (GRH)
20.10.60737313967053584777533030662144.1	x^20 - 18x^18 + 141x^16 - 830x^14 + 3396x^12 - 9432x^10 + 18835x^8 - 16578x^6 - 10413x^4 + 6318x^2 - 351	\( -\,2^{30}\cdot 3^{19}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.0.182211941901160754332599091986432.1	x^20 + 18x^18 + 87x^16 + 156x^14 + 1935x^12 + 11976x^10 + 19095x^8 - 3078x^6 - 14526x^4 + 4860x^2 + 1053	\( 2^{30}\cdot 3^{20}\cdot 13^{5}\cdot 107^{4} \)	20T1023	$[2, 4]$ (GRH)
20.12.182211941901160754332599091986432.1	x^20 - 24x^18 + 210x^16 - 984x^14 + 2985x^12 - 6594x^10 + 10860x^8 - 12186x^6 + 7956x^4 - 2340x^2 + 117	\( 2^{30}\cdot 3^{20}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.0.182211941901160754332599091986432.2	x^20 + 24x^18 + 210x^16 + 984x^14 + 2985x^12 + 6594x^10 + 10860x^8 + 12186x^6 + 7956x^4 + 2340x^2 + 117	\( 2^{30}\cdot 3^{20}\cdot 13^{5}\cdot 107^{4} \)	20T1023	$[2, 2, 2]$ (GRH)
20.12.182211941901160754332599091986432.2	x^20 - 18x^18 + 87x^16 - 156x^14 + 1935x^12 - 11976x^10 + 19095x^8 + 3078x^6 - 14526x^4 - 4860x^2 + 1053	\( 2^{30}\cdot 3^{20}\cdot 13^{5}\cdot 107^{4} \)	20T1023	Trivial (GRH)
20.10.239031657359168112819061279296875.1	x^20 - 8x^19 + 28x^18 - 47x^17 - 85x^16 + 647x^15 - 1190x^14 - 411x^13 + 6142x^12 - 8361x^11 - 6993x^10 + 23763x^9 - 7937x^8 - 19430x^7 + 17201x^6 - 320x^5 - 4795x^4 + 1915x^3 - 150x + 25	\( -\,5^{16}\cdot 11^{5}\cdot 9931^{4} \)	20T1023	Trivial (GRH)
20.6.842574744025230907032098388671875.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1042x^16 - 3032x^15 + 7354x^14 - 15044x^13 + 26107x^12 - 38472x^11 + 47891x^10 - 49854x^9 + 42554x^8 - 28792x^7 + 14447x^6 - 4495x^5 + 154x^4 + 610x^3 - 279x^2 + 45x - 1	\( -\,5^{14}\cdot 11^{4}\cdot 101\cdot 2339^{4}\cdot 3119 \)	20T1023	$[4]$ (GRH)
20.14.2804604340661993478400000000000000.1	x^20 - 11x^18 + 40x^16 - 30x^14 - 132x^12 + 261x^10 - 23x^8 - 190x^6 + 45x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 11^{4}\cdot 2339^{4} \)	20T1023	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)
20.2.2804604340661993478400000000000000.1	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)
20.6.2804604340661993478400000000000000.1	x^20 + 11x^18 + 40x^16 + 30x^14 - 132x^12 - 261x^10 - 23x^8 + 190x^6 + 45x^4 - 9x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 11^{4}\cdot 2339^{4} \)	20T1023	Trivial (GRH)
20.14.5784566108091868330221282958984375.1	x^20 - 2x^19 - 16x^18 + 42x^17 - 36x^16 - 28x^15 + 297x^14 - 2555x^13 + 6196x^12 + 10395x^11 - 40015x^10 + 13490x^9 + 93845x^8 - 94170x^7 - 74560x^6 + 101860x^5 - 6530x^4 - 13455x^3 + 670x^2 + 245x - 5	\( -\,5^{15}\cdot 11^{7}\cdot 9931^{4} \)	20T1023	Trivial (GRH)
20.16.6048917905826368989069024658203125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 146x^16 + 352x^15 - 86x^14 - 764x^13 + 1159x^12 - 12x^11 - 1747x^10 + 1656x^9 + 437x^8 - 1696x^7 + 845x^6 + 401x^5 - 548x^4 + 100x^3 + 54x^2 - 9x - 1	\( 5^{14}\cdot 11^{4}\cdot 2339^{4}\cdot 2261549 \)	20T1023	Trivial (GRH)
20.2.8632085051759631012385809326171875.1	x^20 - x^19 - 4x^18 - 27x^17 + 65x^16 + 181x^15 - 157x^14 - 1498x^13 + 5135x^12 - 14279x^11 + 33862x^10 - 70531x^9 + 123896x^8 - 165225x^7 + 182383x^6 - 148291x^5 + 94004x^4 - 41289x^3 + 13439x^2 - 4786x + 911	\( -\,5^{14}\cdot 11^{4}\cdot 9931^{5} \)	20T1023	$[7]$ (GRH)
20.12.94952935569355941136243902587890625.1	x^20 - 2x^19 - 15x^18 + 2x^17 + 91x^16 + 104x^15 + 204x^14 + 769x^13 - 4205x^12 - 11955x^11 + 393x^10 + 28001x^9 + 80809x^8 + 105143x^7 - 108306x^6 - 376080x^5 - 268435x^4 - 3950x^3 + 58425x^2 + 17500x + 125	\( 5^{14}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.8.94952935569355941136243902587890625.1	x^20 - 4x^19 + 17x^18 - 112x^17 + 297x^16 - 932x^15 + 2985x^14 - 3257x^13 + 539x^12 + 12810x^11 - 85235x^10 + 202230x^9 - 311905x^8 + 408860x^7 - 85475x^6 - 834850x^5 + 1664625x^4 - 2524850x^3 + 3310850x^2 - 2493300x + 735025	\( 5^{14}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.12.94952935569355941136243902587890625.2	x^20 - 2x^19 - 17x^18 + 34x^17 - 5x^16 - 710x^15 + 217x^14 + 5767x^13 + 4271x^12 - 15567x^11 - 23680x^10 + 8761x^9 + 36701x^8 + 14058x^7 - 17130x^6 - 12240x^5 + 3449x^4 + 3889x^3 - 248x^2 - 479x - 19	\( 5^{14}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.8.94952935569355941136243902587890625.2	x^20 - 6x^19 + 19x^18 - 31x^17 + 40x^16 - 286x^15 + 410x^14 - 326x^13 - 7337x^12 + 3281x^11 - 381x^10 + 7101x^9 + 40779x^8 + 16602x^7 - 46928x^6 - 216915x^5 + 92851x^4 + 347098x^3 - 172510x^2 - 139152x + 77411	\( 5^{14}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.18.305701873132157289145600000000000000.1	x^20 - 21x^18 + 184x^16 - 866x^14 + 2332x^12 - 3455x^10 + 2138x^8 + 818x^6 - 1922x^4 + 899x^2 - 109	\( -\,2^{20}\cdot 5^{14}\cdot 11^{4}\cdot 109\cdot 2339^{4} \)	20T1023	Trivial (GRH)
20.12.474764677846779705681219512939453125.1	x^20 - 3x^19 - 30x^18 + 57x^17 + 417x^16 - 393x^15 - 4122x^14 + 4795x^13 + 35632x^12 - 47393x^11 - 236955x^10 + 66599x^9 + 731100x^8 + 523933x^7 - 352102x^6 - 432661x^5 + 136989x^4 + 81080x^3 - 47110x^2 + 10050x - 775	\( 5^{15}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.8.474764677846779705681219512939453125.1	x^20 - 8x^19 + 16x^18 + 18x^17 - 15x^16 - 894x^15 + 2023x^14 + 3986x^13 - 21206x^12 + 35441x^11 + 66354x^10 - 284097x^9 - 179280x^8 + 903183x^7 + 524753x^6 - 1454770x^5 - 841143x^4 + 919508x^3 + 507195x^2 + 25941x + 839	\( 5^{15}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)
20.12.474764677846779705681219512939453125.2	x^20 - 3x^19 - 28x^18 + 75x^17 + 305x^16 - 804x^15 - 1602x^14 + 6014x^13 + 4413x^12 - 39219x^11 - 8747x^10 + 199639x^9 + 7640x^8 - 652342x^7 + 101226x^6 + 1140214x^5 - 364886x^4 - 793637x^3 + 189952x^2 + 188709x + 23291	\( 5^{15}\cdot 11^{5}\cdot 9931^{5} \)	20T1023	Trivial (GRH)