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 56)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.202312357996686362657792.1	x^20 - 4x^19 + x^18 + 12x^17 - 12x^16 + 4x^15 - 7x^14 - 9x^12 + 23x^11 - 33x^10 + 45x^9 - 25x^8 + 7x^7 - 14x^6 + 28x^5 - 33x^4 + 19x^3 - 2x^2 - 3x + 1	\( 2^{10}\cdot 7^{8}\cdot 17^{11} \)	20T426	Trivial (GRH)
20.0.9913305541837631770231808.1	x^20 - 4x^19 + 8x^18 - 10x^17 + 12x^16 - 15x^15 + 13x^14 - 15x^13 + 37x^12 - 40x^11 - 76x^10 + 231x^9 - 142x^8 - 227x^7 + 493x^6 - 327x^5 - x^4 + 103x^3 + 65x^2 + 14x + 1	\( 2^{10}\cdot 7^{10}\cdot 17^{11} \)	20T426	$[2]$ (GRH)
20.0.9913305541837631770231808.2	x^20 - 4x^19 + 4x^18 + 7x^17 - 18x^16 + 10x^15 + 23x^14 - 18x^13 - 9x^12 + 73x^11 + 58x^10 - 55x^9 + 112x^8 + 165x^7 + 108x^6 + 83x^5 + 204x^4 + 176x^3 + 69x^2 + 13x + 1	\( 2^{10}\cdot 7^{10}\cdot 17^{11} \)	20T426	Trivial (GRH)
20.4.58468271461042358808101888.1	x^20 - 4x^19 + x^18 + 7x^17 + 12x^16 - 25x^15 - 24x^14 + 11x^13 + 56x^12 + 91x^11 - 238x^10 + 14x^9 + 41x^8 + 210x^7 - 97x^6 + 10x^5 - 356x^4 + 273x^3 + 196x^2 - 245x + 49	\( 2^{10}\cdot 7^{8}\cdot 17^{13} \)	20T426	Trivial (GRH)
20.12.1198207010758520322015083315072437.1	x^20 - 5x^19 - 14x^18 + 141x^17 - 343x^16 + 50x^15 + 1904x^14 - 5209x^13 + 4433x^12 + 5889x^11 - 17839x^10 + 15105x^9 + 2821x^8 - 17153x^7 + 13978x^6 - 407x^5 - 6246x^4 + 2831x^3 + 405x^2 - 306x - 27	\( 13^{11}\cdot 401^{8} \)	20T426	Trivial (GRH)
20.4.1198207010758520322015083315072437.1	x^20 - 10x^19 + 74x^18 - 381x^17 + 1595x^16 - 5416x^15 + 15470x^14 - 37276x^13 + 75992x^12 - 130718x^11 + 185448x^10 - 210750x^9 + 170528x^8 - 60450x^7 - 87282x^6 + 198081x^5 - 223144x^4 + 165620x^3 - 81549x^2 + 24167x - 2873	\( 13^{11}\cdot 401^{8} \)	20T426	$[2]$ (GRH)
20.16.191976696673085084180853546142578125.1	x^20 - 5x^19 + 20x^18 - 30x^17 - 285x^16 + 974x^15 - 890x^14 + 1610x^13 + 3710x^12 - 30280x^11 + 14616x^10 + 78985x^9 - 53965x^8 - 83990x^7 + 51670x^6 + 46314x^5 - 18255x^4 - 13680x^3 + 1645x^2 + 1665x + 171	\( 5^{15}\cdot 97^{2}\cdot 401^{8} \)	20T426	Trivial (GRH)
20.16.191976696673085084180853546142578125.2	x^20 - 2x^19 - 45x^18 + 83x^17 + 705x^16 - 945x^15 - 5059x^14 + 1666x^13 + 16605x^12 + 33271x^11 - 10497x^10 - 242262x^9 - 90661x^8 + 750086x^7 + 306672x^6 - 1278764x^5 - 517235x^4 + 1203120x^3 + 548219x^2 - 487098x - 269469	\( 5^{15}\cdot 97^{2}\cdot 401^{8} \)	20T426	Trivial (GRH)
20.12.194813520645626483248608015673828125.1	x^20 - 4x^19 - 27x^18 + 194x^17 - 232x^16 - 1739x^15 + 6410x^14 + 3150x^13 - 42307x^12 + 25779x^11 + 105936x^10 - 119589x^9 - 57180x^8 + 106289x^7 - 17734x^6 - 18569x^5 + 9986x^4 - 1983x^3 + 177x^2 - 108x - 9	\( 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	Trivial (GRH)
20.4.194813520645626483248608015673828125.1	x^20 - 4x^19 + 12x^18 - 104x^17 + 258x^16 + 378x^15 - 948x^14 - 5664x^13 + 15540x^12 + 14907x^11 - 134419x^10 + 301534x^9 - 297764x^8 - 169134x^7 + 941416x^6 - 1311498x^5 + 1032859x^4 - 582288x^3 + 241614x^2 - 27090x - 22131	\( 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.8.194813520645626483248608015673828125.1	x^20 - 5x^19 - 8x^18 + 126x^17 - 606x^16 + 949x^15 + 3029x^14 - 16503x^13 + 32014x^12 - 9523x^11 - 88217x^10 + 177933x^9 - 131112x^8 - 7150x^7 + 46116x^6 + 23307x^5 - 20012x^4 - 18411x^3 + 4401x^2 + 5679x + 1251	\( 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2, 2]$ (GRH)
20.12.194813520645626483248608015673828125.2	x^20 - 8x^19 - 11x^18 + 256x^17 - 395x^16 - 2967x^15 + 9767x^14 + 11555x^13 - 87949x^12 + 49241x^11 + 358342x^10 - 626572x^9 - 419884x^8 + 2178107x^7 - 1448287x^6 - 2635848x^5 + 4733767x^4 - 913289x^3 - 3430589x^2 + 2984623x - 759959	\( 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.8.194813520645626483248608015673828125.2	x^20 - 5x^19 + 39x^18 - 34x^17 - 107x^16 + 1115x^15 - 2747x^14 - 11371x^13 + 12282x^12 + 49505x^11 - 924x^10 - 92095x^9 - 55089x^8 + 72007x^7 + 84333x^6 - 16878x^5 - 39049x^4 + 2772x^3 - 6090x^2 - 12933x - 711	\( 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.12.202496984818189934420549080247241853.1	x^20 - 11x^18 - 48x^17 - 102x^16 + 501x^15 + 1905x^14 + 1518x^13 - 9141x^12 - 31062x^11 - 7584x^10 + 115845x^9 + 238607x^8 - 268437x^7 - 769264x^6 + 819072x^5 + 631395x^4 - 1406673x^3 + 94932x^2 + 771768x - 187353	\( 13^{13}\cdot 401^{8} \)	20T426	Trivial (GRH)
20.4.202496984818189934420549080247241853.1	x^20 - 2x^19 - 9x^18 - 4x^17 + 8x^16 + 311x^15 - 1013x^14 - 2943x^13 + 2836x^12 + 5359x^11 - 2238x^10 - 73783x^9 - 72009x^8 + 57368x^7 + 184507x^6 + 197227x^5 - 131553x^4 - 277651x^3 + 17648x^2 + 98838x + 29241	\( 13^{13}\cdot 401^{8} \)	20T426	$[2, 2]$ (GRH)
20.8.202496984818189934420549080247241853.1	x^20 - 2x^19 - 2x^18 - 18x^17 - 86x^16 + 442x^15 + 234x^14 + 270x^13 - 4712x^12 - 3007x^11 + 16087x^10 - 14265x^9 + 29975x^8 - 33568x^7 + 98555x^6 - 261751x^5 + 208699x^4 - 81046x^3 + 97592x^2 - 56310x + 9099	\( 13^{13}\cdot 401^{8} \)	20T426	$[2]$ (GRH)
20.8.202496984818189934420549080247241853.2	x^20 + 2x^18 - 49x^17 - 92x^16 - 67x^15 + 29x^14 + 1402x^13 + 347x^12 + 1490x^11 - 6877x^10 - 4260x^9 + 28512x^8 + 17533x^7 + 66422x^6 - 81651x^5 + 91742x^4 - 812x^3 - 227354x^2 - 44016x - 711	\( 13^{13}\cdot 401^{8} \)	20T426	$[2]$ (GRH)
20.12.1753321685810638349237472141064453125.1	x^20 - 8x^19 - 7x^18 + 207x^17 - 394x^16 - 1468x^15 + 5814x^14 + 1761x^13 - 31742x^12 + 24039x^11 + 88202x^10 - 123986x^9 - 132368x^8 + 257416x^7 + 93723x^6 - 346819x^5 - 260864x^4 - 65625x^3 - 6201x^2 - 99x + 9	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	Trivial (GRH)
20.4.1753321685810638349237472141064453125.1	x^20 - 5x^19 + 49x^18 - 163x^17 + 669x^16 - 1520x^15 + 1571x^14 - 329x^13 - 28502x^12 + 84298x^11 - 225519x^10 + 516232x^9 - 688895x^8 + 970940x^7 - 742381x^6 + 56136x^5 + 999706x^4 - 1205067x^3 + 1568454x^2 - 1370685x + 786559	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2, 2]$ (GRH)
20.8.1753321685810638349237472141064453125.1	x^20 - 5x^19 + 11x^18 + 22x^17 - 314x^16 + 918x^15 - 919x^14 - 2712x^13 + 13715x^12 - 20534x^11 + 3142x^10 + 51084x^9 - 138550x^8 + 137657x^7 + 56747x^6 - 131853x^5 - 148436x^4 - 34890x^3 + 173745x^2 - 36765x - 8469	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.12.1753321685810638349237472141064453125.2	x^20 - 7x^19 - 18x^18 + 234x^17 - 210x^16 - 2945x^15 + 7088x^14 + 17195x^13 - 62178x^12 - 62496x^11 + 239526x^10 + 388717x^9 - 237833x^8 - 2069502x^7 - 1925805x^6 + 2353437x^5 + 6208866x^4 + 5565915x^3 - 660015x^2 - 3782700x - 1095525	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	Trivial (GRH)
20.8.1753321685810638349237472141064453125.2	x^20 - 8x^19 + 38x^18 - 226x^17 + 945x^16 - 3205x^15 + 12198x^14 - 33416x^13 + 80512x^12 - 229690x^11 + 454875x^10 - 1064806x^9 + 3406720x^8 - 7442088x^7 + 16577353x^6 - 33069267x^5 + 31934522x^4 - 3483430x^3 - 13841592x^2 + 6355544x - 417919	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.12.1753321685810638349237472141064453125.3	x^20 - 8x^19 + 2x^18 + 168x^17 - 635x^16 + 91x^15 + 5138x^14 - 10945x^13 + 34x^12 - 9343x^11 + 164539x^10 - 255161x^9 - 607343x^8 + 1757562x^7 + 102034x^6 - 3267388x^5 + 1266084x^4 + 2415120x^3 - 1168449x^2 - 669901x + 243241	\( 3^{10}\cdot 5^{11}\cdot 239^{10} \)	20T426	Trivial (GRH)
20.8.3280906026328914297094848663330078125.3	x^20 - x^19 - 22x^18 + 103x^17 - 339x^16 + 251x^15 + 2166x^14 - 7737x^13 + 13339x^12 + 31738x^11 - 170685x^10 + 54973x^9 + 571581x^8 - 967984x^7 - 11999x^6 + 3098069x^5 - 2474812x^4 - 5082669x^3 + 2800900x^2 + 4193337x + 559701	\( 5^{15}\cdot 401^{10} \)	20T426	Trivial (GRH)
20.8.3280906026328914297094848663330078125.4	x^20 - x^19 - 25x^18 - 19x^17 + 105x^16 + 695x^15 + 1144x^14 - 1048x^13 - 20445x^12 + 50238x^11 - 144458x^10 + 438711x^9 - 1052756x^8 + 1473553x^7 - 2143907x^6 + 3488487x^5 - 3408590x^4 + 1298090x^3 + 448726x^2 - 312951x + 14211	\( 5^{15}\cdot 401^{10} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.1	x^20 - 3x^18 - 52x^16 + 298x^14 - 164x^12 - 2125x^10 + 5018x^8 - 1838x^6 - 4886x^4 + 4065x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.16.3576211589862019840319539200000000000.1	x^20 - 34x^18 + 399x^16 - 1921x^14 + 1994x^12 + 12846x^10 - 35651x^8 + 11474x^6 + 17511x^4 - 6805x^2 + 605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.1	x^20 + 6x^18 - 146x^16 + 155x^14 + 1784x^12 + 367x^10 - 4230x^8 - 2525x^6 + 2284x^4 + 2070x^2 + 405	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.2	x^20 - 130x^16 - 493x^14 + 601x^12 + 2530x^10 - 1234x^8 - 1174x^6 + 739x^4 - 120x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.16.3576211589862019840319539200000000000.2	x^20 - 27x^18 + 222x^16 - 570x^14 - 948x^12 + 7124x^10 - 10809x^8 + 1342x^6 + 8149x^4 - 4600x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.2	x^20 + 14x^18 - 19x^16 - 368x^14 + 243x^12 + 1400x^10 - 543x^8 - 1536x^6 + 219x^4 + 135x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.3	x^20 - 29x^18 + 289x^16 - 1015x^14 - 381x^12 + 6527x^10 - 2685x^8 - 8245x^6 - 1771x^4 - 5x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.3	x^20 + 12x^18 - 27x^16 - 606x^14 - 453x^12 + 5956x^10 + 4470x^8 - 3376x^6 - 326x^4 + 55x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.4	x^20 + 7x^18 - 182x^16 - 49x^14 + 9316x^12 - 40855x^10 + 57220x^8 - 12583x^6 - 9461x^4 + 300x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.4	x^20 + 3x^18 - 223x^16 - 2477x^14 - 9377x^12 - 9301x^10 + 16313x^8 + 25396x^6 + 4426x^4 - 2715x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	$[2]$ (GRH)
20.12.3576211589862019840319539200000000000.5	x^20 - 10x^18 - 9x^16 + 336x^14 - 762x^12 - 847x^10 + 2726x^8 + 42x^6 - 1696x^4 - 225x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.5	x^20 + 10x^18 - 9x^16 - 336x^14 - 762x^12 + 847x^10 + 2726x^8 - 42x^6 - 1696x^4 + 225x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.6	x^20 - 14x^18 - 19x^16 + 368x^14 + 243x^12 - 1400x^10 - 543x^8 + 1536x^6 + 219x^4 - 135x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.6	x^20 + 12x^18 - 10x^16 - 413x^14 - 226x^12 + 3958x^10 + 2330x^8 - 10487x^6 - 1054x^4 + 2825x^2 + 605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	$[2]$ (GRH)
20.12.3576211589862019840319539200000000000.7	x^20 - 11x^18 - 57x^16 + 975x^14 - 2541x^12 - 2534x^10 + 9653x^8 - 3369x^6 - 3196x^4 + 1125x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.7	x^20 - 265x^16 - 1366x^14 + 4811x^12 + 32390x^10 + 31619x^8 + 5822x^6 - 751x^4 - 95x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.8	x^20 + 7x^18 - 30x^16 - 28x^14 + 158x^12 - 63x^10 - 147x^8 + 114x^6 + 9x^4 - 25x^2 + 5	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.8.3576211589862019840319539200000000000.8	x^20 + 24x^18 + 128x^16 - 319x^14 - 3032x^12 - 548x^10 + 12767x^8 + 1187x^6 - 10844x^4 + 3450x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.12.3576211589862019840319539200000000000.9	x^20 - 12x^18 - 28x^16 + 668x^14 - 692x^12 - 9716x^10 + 20288x^8 + 12161x^6 - 20669x^4 - 675x^2 + 125	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{8} \)	20T426	Trivial (GRH)
20.20.823070770673063523939149301768798828125.1	x^20 - 6x^19 - 68x^18 + 546x^17 + 790x^16 - 15528x^15 + 27509x^14 + 121115x^13 - 534817x^12 + 534768x^11 + 742976x^10 - 1898411x^9 + 659006x^8 + 1365776x^7 - 1231009x^6 - 10130x^5 + 355693x^4 - 131936x^3 + 14573x^2 - 486x - 1	\( 5^{13}\cdot 19^{10}\cdot 43^{8}\cdot 97^{2} \)	20T426	Trivial (GRH)
20.20.823070770673063523939149301768798828125.2	x^20 - 4x^19 - 61x^18 + 200x^17 + 1369x^16 - 3916x^15 - 15219x^14 + 38099x^13 + 95351x^12 - 201486x^11 - 354586x^10 + 594912x^9 + 771844x^8 - 963875x^7 - 901175x^6 + 821513x^5 + 477805x^4 - 335464x^3 - 87875x^2 + 43985x + 3781	\( 5^{13}\cdot 19^{10}\cdot 43^{8}\cdot 97^{2} \)	20T426	Trivial (GRH)
20.0.204276782224508435298892398643200000000000.1	x^20 + 103x^18 + 3949x^16 + 76751x^14 + 838833x^12 + 5275520x^10 + 18436683x^8 + 32414147x^6 + 24403334x^4 + 6755335x^2 + 285605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2, 2, 59048]$ (GRH)
20.12.204276782224508435298892398643200000000000.1	x^20 + 32x^18 - 6378x^14 - 28602x^12 + 176547x^10 + 325483x^8 - 2201416x^6 + 3023589x^4 - 1594130x^2 + 285605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.16.204276782224508435298892398643200000000000.1	x^20 - 58x^18 + 673x^16 + 7078x^14 - 106359x^12 + 486685x^10 - 1038672x^8 + 977032x^6 - 39196x^4 - 571210x^2 + 285605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)
20.4.204276782224508435298892398643200000000000.1	x^20 + 81x^18 + 1476x^16 - 13869x^14 - 550206x^12 - 4926311x^10 - 18639312x^8 - 28947445x^6 - 8095169x^4 + 11820940x^2 + 285605	\( 2^{20}\cdot 3^{8}\cdot 5^{11}\cdot 239^{10} \)	20T426	$[2]$ (GRH)