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 96)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.3814697265625000000000000.2	x^20 + 10x^18 + 45x^16 + 120x^14 + 210x^12 + 251x^10 + 205x^8 + 110x^6 + 35x^4 + 5x^2 - 1	\( -\,2^{12}\cdot 5^{30} \)	20T513	Trivial (GRH)
20.0.4360000000000000000000000.1	x^20 + 5x^16 - 8x^15 + 40x^12 - 20x^11 - 42x^10 + 70x^8 - 40x^7 - 60x^6 + 12x^5 + 55x^4 - 10x^2 + 1	\( 2^{24}\cdot 5^{22}\cdot 109 \)	20T513	Trivial
20.2.19073486328125000000000000.1	x^20 + 5x^18 + 10x^16 + 45x^14 + 210x^12 + 245x^10 + 100x^8 - 25x^6 - 100x^4 - 25x^2 - 5	\( -\,2^{12}\cdot 5^{31} \)	20T513	Trivial (GRH)
20.4.21800000000000000000000000.1	x^20 - 5x^18 - 10x^17 + 25x^16 + 38x^15 - 50x^14 - 160x^13 + 195x^12 + 240x^11 - 301x^10 - 440x^9 + 675x^8 + 190x^7 - 680x^6 + 82x^5 + 425x^4 - 210x^3 - 85x^2 + 90x - 19	\( 2^{24}\cdot 5^{23}\cdot 109 \)	20T513	Trivial (GRH)
20.4.69760000000000000000000000.1	x^20 - 20x^16 - 36x^15 - 50x^14 - 120x^13 - 100x^12 + 120x^11 + 500x^10 + 1100x^9 + 1740x^8 + 1960x^7 + 1580x^6 + 992x^5 + 600x^4 + 360x^3 + 160x^2 + 40x + 4	\( 2^{28}\cdot 5^{22}\cdot 109 \)	20T513	Trivial (GRH)
20.0.189190725171448873364750336.1	x^20 - 6x^19 + 15x^18 - 16x^17 - 5x^16 + 26x^15 + 40x^14 - 330x^13 + 905x^12 - 1546x^11 + 1817x^10 - 1504x^9 + 831x^8 - 116x^7 - 350x^6 + 284x^5 + 153x^4 - 356x^3 + 159x^2 + 10x + 1	\( 2^{28}\cdot 13^{14}\cdot 179 \)	20T513	Trivial (GRH)
20.8.1537414689913008558084697161728.1	x^20 - 7x^19 + 16x^18 + 7x^17 - 116x^16 + 257x^15 - 198x^14 - 275x^13 + 1033x^12 - 1484x^11 + 1114x^10 + 10x^9 - 849x^8 + 1469x^7 - 394x^6 + 261x^5 + 442x^4 - 251x^3 - 26x^2 + 13x + 1	\( 2^{16}\cdot 17\cdot 53^{14} \)	20T513	Trivial (GRH)
20.12.2622648588675132246144483393536.1	x^20 - 7x^19 + 12x^18 + 20x^17 - 85x^16 + 82x^15 - 95x^14 + 448x^13 - 714x^12 - 279x^11 + 1705x^10 - 176x^9 - 2075x^8 - 1931x^7 + 3399x^6 + 1867x^5 - 1883x^4 - 332x^3 + 320x^2 - 12x - 4	\( 2^{16}\cdot 29\cdot 53^{14} \)	20T513	Trivial (GRH)
20.14.3689472640000000000000000000000.3	x^20 - 15x^18 + 45x^16 + 130x^14 - 595x^12 - 81x^10 + 2015x^8 - 1070x^6 - 1985x^4 + 1665x^2 - 81	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.3689472640000000000000000000000.3	x^20 - 40x^16 - 60x^14 + 400x^12 + 1204x^10 + 880x^8 - 240x^6 - 480x^4 - 160x^2 - 16	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.14.3689472640000000000000000000000.4	x^20 - 40x^16 + 60x^14 + 400x^12 - 1204x^10 + 880x^8 + 240x^6 - 480x^4 + 160x^2 - 16	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.3689472640000000000000000000000.4	x^20 + 15x^18 + 45x^16 - 130x^14 - 595x^12 + 81x^10 + 2015x^8 + 1070x^6 - 1985x^4 - 1665x^2 - 81	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.10.3689472640000000000000000000000.6	x^20 - 15x^18 + 65x^16 - 10x^14 - 395x^12 + 239x^10 + 595x^8 + 130x^6 - 45x^4 - 15x^2 - 1	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.10.3689472640000000000000000000000.7	x^20 + 15x^18 + 65x^16 + 10x^14 - 395x^12 - 239x^10 + 595x^8 - 130x^6 - 45x^4 + 15x^2 - 1	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.1	x^20 + 15x^18 + 15x^16 - 435x^14 - 160x^12 + 4519x^10 - 8095x^8 + 4705x^6 - 145x^4 - 420x^2 - 16	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.2	x^20 - 65x^16 - 15x^14 + 1295x^12 - 79x^10 - 9485x^8 + 4380x^6 + 16240x^4 - 4160x^2 - 256	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.3	x^20 - 5x^18 - 15x^16 + 85x^14 + 25x^12 - 271x^10 + 80x^8 + 105x^6 - 10x^4 - 10x^2 - 1	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.4	x^20 - 60x^16 + 70x^14 + 975x^12 - 1714x^10 - 4070x^8 + 7020x^6 + 5885x^4 - 6610x^2 - 3481	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.5	x^20 + 5x^18 - 80x^16 - 325x^14 + 1050x^12 + 244x^10 - 865x^8 - 80x^6 + 125x^4 - 10x^2 - 1	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.10.14533256019141235351562500000000.6	x^20 + 20x^18 + 75x^16 - 410x^14 - 1160x^12 + 4780x^10 - 3125x^8 - 1900x^6 + 1500x^4 + 100x^2 - 25	\( -\,2^{8}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.12.24598635038608136929355154587648.1	x^20 - 4x^19 - 9x^18 + 36x^17 + 9x^16 - 48x^15 + 102x^14 - 292x^13 + 179x^12 + 736x^11 - 2859x^10 - 46x^9 + 4496x^8 - 4006x^7 - 1874x^6 + 6328x^5 + 1067x^4 - 3058x^3 - 916x^2 + 146x + 29	\( 2^{20}\cdot 17\cdot 53^{14} \)	20T513	Trivial (GRH)
20.8.41962377418802115938311734296576.1	x^20 - 4x^19 - 7x^18 + 10x^17 + 84x^16 + 46x^15 - 268x^14 - 930x^13 + 1627x^12 + 202x^11 + 3184x^10 - 10874x^9 - 667x^8 + 42398x^7 - 81637x^6 + 77324x^5 - 39280x^4 + 8932x^3 + 422x^2 - 720x + 153	\( 2^{20}\cdot 29\cdot 53^{14} \)	20T513	Trivial (GRH)
20.10.59031562240000000000000000000000.1	x^20 + 5x^18 - 55x^16 - 110x^14 + 765x^12 + 671x^10 - 3045x^8 - 350x^6 + 115x^4 + 5x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.14.59031562240000000000000000000000.1	x^20 - 5x^18 - 55x^16 + 340x^14 + 295x^12 - 5579x^10 + 13265x^8 - 10070x^6 - 1975x^4 + 4465x^2 - 961	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.18.59031562240000000000000000000000.1	x^20 - 15x^18 + 75x^16 - 90x^14 - 405x^12 + 1481x^10 - 1875x^8 + 1100x^6 - 305x^4 + 35x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.2.59031562240000000000000000000000.1	x^20 + 15x^18 + 75x^16 + 90x^14 - 405x^12 - 1481x^10 - 1875x^8 - 1100x^6 - 305x^4 - 35x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.59031562240000000000000000000000.1	x^20 - 65x^16 - 60x^14 + 650x^12 + 616x^10 - 830x^8 - 1140x^6 - 395x^4 - 40x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.10.59031562240000000000000000000000.2	x^20 - 25x^16 + 20x^14 + 130x^12 - 64x^10 - 230x^8 - 20x^6 + 45x^4 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.14.59031562240000000000000000000000.2	x^20 - 10x^18 + 15x^16 + 100x^14 - 230x^12 - 236x^10 + 610x^8 + 140x^6 - 315x^4 + 70x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.59031562240000000000000000000000.2	x^20 + 15x^18 + 45x^16 - 240x^14 - 1185x^12 + 205x^10 + 4225x^8 + 2950x^6 - 1075x^4 - 775x^2 - 25	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.14.59031562240000000000000000000000.3	x^20 - 65x^16 + 60x^14 + 650x^12 - 616x^10 - 830x^8 + 1140x^6 - 395x^4 + 40x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.59031562240000000000000000000000.3	x^20 + 5x^18 - 55x^16 - 340x^14 + 295x^12 + 5579x^10 + 13265x^8 + 10070x^6 - 1975x^4 - 4465x^2 - 961	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.14.59031562240000000000000000000000.4	x^20 - 5x^18 - 85x^16 + 390x^14 - 265x^12 - 981x^10 + 1905x^8 - 1200x^6 + 235x^4 + 5x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.6.59031562240000000000000000000000.4	x^20 + 5x^18 - 85x^16 - 390x^14 - 265x^12 + 981x^10 + 1905x^8 + 1200x^6 + 235x^4 - 5x^2 - 1	\( -\,2^{32}\cdot 5^{22}\cdot 7^{8} \)	20T513	Trivial (GRH)
20.10.92606626027701221381101758447616.1	x^20 - 12x^18 - 21x^16 + 354x^14 - 2x^12 - 1324x^10 + 28x^8 + 1568x^6 + 64x^4 - 576x^2 - 64	\( -\,2^{26}\cdot 53^{14} \)	20T513	Trivial (GRH)
20.10.92606626027701221381101758447616.2	x^20 + 2x^18 - 40x^16 - 68x^14 + 457x^12 + 654x^10 - 2022x^8 - 2356x^6 + 3020x^4 + 2720x^2 - 64	\( -\,2^{26}\cdot 53^{14} \)	20T513	Trivial (GRH)
20.18.95749736674107392000000000000000.1	x^20 - 25x^18 + 181x^16 - 462x^14 - 11x^12 + 1929x^10 - 3269x^8 + 2330x^6 - 785x^4 + 115x^2 - 5	\( -\,2^{28}\cdot 5^{15}\cdot 43^{8} \)	20T513	Trivial (GRH)
20.2.95749736674107392000000000000000.1	x^20 + 25x^18 + 181x^16 + 462x^14 - 11x^12 - 1929x^10 - 3269x^8 - 2330x^6 - 785x^4 - 115x^2 - 5	\( -\,2^{28}\cdot 5^{15}\cdot 43^{8} \)	20T513	Trivial (GRH)
20.10.225057831040000000000000000000000.1	x^20 - 65x^16 - 160x^14 + 570x^12 + 1696x^10 - 1010x^8 - 3680x^6 + 565x^4 + 1120x^2 - 61	\( -\,2^{28}\cdot 5^{22}\cdot 7^{8}\cdot 61 \)	20T513	Trivial (GRH)
20.10.232532096306259765625000000000000.1	x^20 + 10x^18 - 60x^16 - 490x^14 + 1910x^12 + 4914x^10 - 21355x^8 + 1480x^6 + 39695x^4 - 10380x^2 - 15376	\( -\,2^{12}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.14.232532096306259765625000000000000.1	x^20 + 5x^18 - 50x^16 - 110x^14 + 1065x^12 - 724x^10 - 5745x^8 + 13470x^6 - 10790x^4 + 2815x^2 - 1	\( -\,2^{12}\cdot 5^{22}\cdot 47^{8} \)	20T513	Trivial (GRH)
20.6.232532096306259765625000000000000.1	x^20 + 15x^18 + 40x^16 - 265x^14 - 1495x^12 - 1784x^10 + 1535x^8 + 2905x^6 + 480x^4 - 135x^2 - 1	\( -\,2^{12}\cdot 5^{22}\cdot 47^{8} \)	20T513	$[2]$ (GRH)
20.16.356788037640781250000000000000000.1	x^20 - 10x^19 + 40x^18 - 75x^17 + 25x^16 + 208x^15 - 490x^14 + 300x^13 + 610x^12 - 1190x^11 + 292x^10 + 1020x^9 - 935x^8 - 150x^7 + 600x^6 - 161x^5 - 160x^4 + 60x^3 + 20x^2 - 5x - 1	\( 2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 41\cdot 9661 \)	20T513	Trivial (GRH)
20.12.393578160617730190869682473402368.1	x^20 - 4x^19 - 7x^18 + 16x^17 + 60x^16 + 72x^15 - 416x^14 - 578x^13 + 1877x^12 + 1054x^11 - 5071x^10 - 108x^9 + 6680x^8 - 1598x^7 - 3856x^6 + 1524x^5 + 789x^4 - 426x^3 - 27x^2 + 38x - 4	\( 2^{24}\cdot 17\cdot 53^{14} \)	20T513	Trivial (GRH)
20.12.393578160617730190869682473402368.2	x^20 - 9x^18 - 112x^16 + 1045x^14 - 273x^12 - 4700x^10 - 797x^8 + 3529x^6 + 588x^4 - 585x^2 + 17	\( 2^{24}\cdot 17\cdot 53^{14} \)	20T513	Trivial (GRH)
20.12.444312845384859473286477479739392.2	x^20 - 4x^19 - 10x^18 + 52x^17 - 70x^16 + 28x^15 + 1406x^14 - 4800x^13 - 727x^12 + 15684x^11 - 5674x^10 - 16280x^9 + 4480x^8 + 5232x^7 + 3832x^6 - 300x^5 - 2937x^4 - 328x^3 + 408x^2 + 32x - 16	\( 2^{16}\cdot 17^{3}\cdot 53^{14} \)	20T513	Trivial (GRH)
20.8.671398038700833855012987748745216.1	x^20 - 3x^19 - 2x^18 - 2x^17 + 45x^16 + 138x^15 - 170x^14 - 1666x^13 + 1167x^12 + 6641x^11 - 8422x^10 + 3682x^9 - 13303x^8 + 19388x^7 - 8276x^6 + 6668x^5 - 9051x^4 + 2155x^3 + 1032x^2 + 8x - 1	\( 2^{24}\cdot 29\cdot 53^{14} \)	20T513	Trivial (GRH)
20.8.671398038700833855012987748745216.2	x^20 - 4x^19 - 16x^18 + 59x^17 + 93x^16 - 270x^15 - 134x^14 + 284x^13 - 737x^12 + 1092x^11 + 3202x^10 - 3441x^9 - 3767x^8 + 4958x^7 + 2348x^6 + 2x^5 + 2682x^4 - 640x^3 - 1004x^2 + 564x - 68	\( 2^{24}\cdot 29\cdot 53^{14} \)	20T513	Trivial (GRH)
20.12.1147425991040000000000000000000000.1	x^20 - 20x^18 + 115x^16 - 80x^14 - 1110x^12 + 2472x^10 + 1670x^8 - 7440x^6 + 2085x^4 + 3020x^2 + 311	\( 2^{28}\cdot 5^{22}\cdot 7^{8}\cdot 311 \)	20T513	Trivial (GRH)
20.8.1147425991040000000000000000000000.1	x^20 + 20x^18 + 115x^16 + 80x^14 - 1110x^12 - 2472x^10 + 1670x^8 + 7440x^6 + 2085x^4 - 3020x^2 + 311	\( 2^{28}\cdot 5^{22}\cdot 7^{8}\cdot 311 \)	20T513	Trivial (GRH)