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 345)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.3219905755813179726837607.1	x^21 - 5x^14 - 8x^7 - 1	\( -\,7^{29} \)	$C_3\times D_7$ (as 21T3)	Trivial (GRH)
21.3.3960879820606443846053527.1	x^21 - 5x^20 + 11x^19 - 20x^18 + 37x^17 - 68x^16 + 120x^15 - 168x^14 + 237x^13 - 331x^12 + 362x^11 - 431x^10 + 452x^9 - 381x^8 + 350x^7 - 238x^6 + 169x^5 - 90x^4 + 43x^3 + 6x^2 + 27	\( -\,13^{2}\cdot 1801^{2}\cdot 193327^{3} \)	21T139	Trivial (GRH)
21.3.6826740523487474380439552.1	x^21 - 2x^20 - x^19 - 3x^18 + 10x^17 + 13x^16 + x^15 - 27x^14 - 16x^13 - 20x^12 + 55x^11 - 4x^10 + 8x^9 - 32x^8 - x^7 + 70x^6 - 52x^5 - 4x^4 + 6x^3 + 2x^2 - 6x + 1	\( -\,2^{21}\cdot 71^{10} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.3.7174552902718171733819392.1	x^21 - 7x^20 + 21x^19 - 42x^18 + 77x^17 - 126x^16 + 168x^15 - 213x^14 + 266x^13 - 280x^12 + 259x^11 - 217x^10 + 133x^9 - 42x^8 - 53x^7 + 126x^6 - 112x^5 + 7x^4 + 63x^3 - 49x^2 + 14x - 1	\( -\,2^{18}\cdot 7^{23} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.9284127557257563917891699.1	x^21 - 5x^20 + 11x^19 - 13x^18 + 7x^17 + 4x^16 - 16x^15 + 13x^14 - 6x^13 + 2x^12 - 2x^11 + 21x^10 - 28x^8 + 29x^7 - 16x^6 - 18x^5 + 17x^4 - 9x^3 - 2x^2 + 3x - 1	\( -\,11^{9}\cdot 13^{14} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.10904210824444953500612167.1	x^21 + x^19 - 2x^18 - 2x^17 - 3x^16 - x^15 + 4x^14 + 15x^13 + 3x^12 - 4x^11 - 29x^10 - 4x^9 + 12x^8 + 23x^7 + 16x^6 - 4x^5 - 7x^4 - 8x^3 - x^2 + 1	\( -\,31^{8}\cdot 67^{3}\cdot 349^{3} \)	21T74	Trivial (GRH)
21.3.65701728236743660173798567.1	x^21 - 4x^20 + 12x^19 - 22x^18 + 41x^17 - 54x^16 + 79x^15 - 60x^14 + 57x^13 + 46x^12 - 70x^11 + 222x^10 - 182x^9 + 306x^8 - 168x^7 + 207x^6 - 48x^5 + 42x^4 + 5x^3 - 17x^2 - 15x - 1	\( -\,3^{24}\cdot 7^{17} \)	$C_3\times F_7$ (as 21T9)	Trivial (GRH)
21.3.108608979330127274981177223.1	x^21 - 9x^14 - 12x^7 + 1	\( -\,3^{28}\cdot 7^{15} \)	$C_3\times F_7$ (as 21T9)	Trivial (GRH)
21.3.167297208611536987435565056.1	x^21 - 7x^20 + 23x^19 - 46x^18 + 59x^17 - 38x^16 - 51x^15 + 276x^14 - 725x^13 + 1392x^12 - 2056x^11 + 2397x^10 - 2311x^9 + 1987x^8 - 1615x^7 + 1208x^6 - 783x^5 + 436x^4 - 201x^3 + 66x^2 - 12x + 1	\( -\,2^{18}\cdot 17^{6}\cdot 31^{9} \)	21T57	Trivial (GRH)
21.3.188012010050973537326115059.1	x^21 - 3x^20 + 2x^19 - 4x^18 + 10x^17 - 9x^16 + 70x^15 - 167x^14 + 91x^13 + 110x^12 - 252x^11 + 50x^10 + 456x^9 - 519x^8 + x^7 + 487x^6 - 548x^5 + 272x^4 - 48x^3 + x^2 - 3x + 1	\( -\,59^{8}\cdot 10859^{3} \)	21T74	Trivial (GRH)
21.3.214407920026380373514939807.1	x^21 - x^20 - x^19 + x^18 - x^17 + 6x^16 - 7x^15 + 2x^14 - 4x^13 + 5x^12 + 9x^11 - 17x^10 + 11x^9 - 4x^8 - 3x^7 + 9x^6 - 6x^5 - x^4 + 3x^3 - x^2 - x + 1	\( -\,184607^{5} \)	21T38	Trivial (GRH)
21.3.270061427296836406180775407.1	x^21 - 4x^18 - x^17 + x^16 + 7x^15 + x^14 - 6x^13 - 11x^12 + 2x^11 + 10x^10 + 14x^9 - 2x^8 - 5x^7 - 6x^6 + 2x^5 - 2x^4 - 3x^3 + 2x^2 - 1	\( -\,193327^{5} \)	21T38	Trivial (GRH)
21.3.336444035684435024524918784.1	x^21 - 5x^20 + 11x^19 - 5x^18 - 29x^17 + 64x^16 - 22x^15 - 117x^14 + 218x^13 - 124x^12 - 76x^11 + 132x^10 - 38x^9 + 31x^8 - 168x^7 + 204x^6 - 47x^5 - 120x^4 + 134x^3 - 63x^2 + 13x - 1	\( -\,2^{14}\cdot 11^{13}\cdot 29^{6} \)	21T57	Trivial (GRH)
21.3.930871627030827422699634607.1	x^21 - 5x^20 + 36x^18 - 35x^17 - 108x^16 + 155x^15 + 176x^14 - 338x^13 - 129x^12 + 413x^11 - 50x^10 - 234x^9 + 162x^8 - 66x^7 - 51x^6 + 196x^5 - 92x^4 - 98x^3 + 71x^2 - 10x - 25	\( -\,151^{2}\cdot 2377^{2}\cdot 193327^{3} \)	21T139	Trivial (GRH)
21.3.4266945093472415611428661007.1	x^21 - x^20 - 7x^19 + 6x^18 + 16x^17 - 27x^16 + 3x^15 + 119x^14 + 23x^13 - 181x^12 - 153x^11 + 154x^10 + 417x^9 - 133x^8 - 395x^7 + 153x^6 + 61x^5 - 33x^4 + 2x^3 + 7x^2 - 2x - 1	\( -\,7^{14}\cdot 184607^{3} \)	21T56	Trivial (GRH)
21.3.4297390112987454978404646912.1	x^21 - x^20 + 9x^19 - 7x^18 + 35x^17 - 27x^16 + 83x^15 - 61x^14 + 123x^13 - 111x^12 + 163x^11 - 225x^10 + 213x^9 - 253x^8 + 177x^7 - 167x^6 + 192x^5 - 180x^4 + 136x^3 - 76x^2 - 12x + 4	\( -\,2^{38}\cdot 3^{18}\cdot 7^{9} \)	$SO(3,7)$ (as 21T20)	Trivial (GRH)
21.3.4900609474961156001559784767.1	x^21 - x^20 - 2x^19 + 9x^18 - 8x^17 - 16x^16 + 40x^15 + 25x^14 - 4x^13 - 178x^12 - 112x^11 + 286x^10 + 394x^9 - 392x^8 - 175x^7 + 201x^6 - 68x^5 - 36x^4 + 30x^3 - 4x^2 - 4x + 1	\( -\,7^{14}\cdot 193327^{3} \)	21T56	Trivial (GRH)
21.3.7146646609494406531041460224.1	x^21 - 3x^20 - 4x^19 + 16x^18 - 9x^17 - 33x^16 + 52x^15 + 12x^14 - 136x^13 + 96x^12 + 180x^11 - 260x^10 - 144x^9 + 312x^8 + 44x^7 - 220x^6 + 15x^5 + 59x^4 - 16x^3 + 36x^2 - 31x + 1	\( -\,2^{64}\cdot 3^{18} \)	$SO(3,7)$ (as 21T20)	Trivial (GRH)
21.3.8971378199137136745057872231.1	x^21 - x^20 + 3x^19 + 4x^18 + 8x^17 - 12x^16 + 9x^15 + 113x^14 - 287x^13 + 404x^12 - 526x^11 + 1106x^10 - 2438x^9 + 2381x^8 - 2385x^7 + 3637x^6 - 6756x^5 + 4734x^4 - 3615x^3 + 1513x^2 - 2017x - 1319	\( -\,7^{2}\cdot 13^{2}\cdot 71^{9}\cdot 4861^{2} \)	21T76	Trivial (GRH)
21.3.10367263422675536780303271503.1	x^21 - 6x^20 - x^19 + 72x^18 - 100x^17 - 299x^16 + 733x^15 + 386x^14 - 2195x^13 + 634x^12 + 3126x^11 - 2357x^10 - 2090x^9 + 2868x^8 + 87x^7 - 1535x^6 + 673x^5 + 170x^4 - 243x^3 + 89x^2 - 15x + 1	\( -\,11^{4}\cdot 103^{4}\cdot 184607^{3} \)	21T130	Trivial (GRH)
21.3.19019216778782670169504453271.1	x^21 - 9x^20 + 23x^19 + 24x^18 - 196x^17 + 152x^16 + 587x^15 - 1008x^14 - 562x^13 + 2180x^12 - 404x^11 - 2259x^10 + 1317x^9 + 1079x^8 - 1081x^7 - 177x^6 + 477x^5 - 106x^4 - 81x^3 + 53x^2 - 12x + 1	\( -\,67^{2}\cdot 71^{9}\cdot 9613^{2} \)	21T76	Trivial (GRH)
21.3.20735011601517857380131405824.1	x^21 - 4x^20 + 8x^19 - 12x^18 + 12x^17 - 16x^16 + 44x^15 - 94x^14 + 160x^13 - 200x^12 + 184x^11 - 132x^10 + 52x^9 - 8x^7 + 4x^6 + 16x^4 - 36x^3 + 32x^2 - 16x + 4	\( -\,2^{20}\cdot 11^{7}\cdot 317^{6} \)	21T27	Trivial (GRH)
21.3.20735011601517857380131405824.2	x^21 - 2x^20 + 2x^19 - 4x^16 - 6x^15 + 8x^14 - 16x^13 + 30x^12 - 24x^11 + 22x^10 - 48x^9 - 4x^8 - 30x^7 + 8x^6 - 4x^5 - 12x^4 - 10x^3 + 12x^2 - 4x + 2	\( -\,2^{20}\cdot 11^{7}\cdot 317^{6} \)	21T27	Trivial (GRH)
21.3.31095511042786085990206459319.1	x^21 - x^20 - 7x^19 + 6x^18 + 3x^17 - 30x^16 + 72x^15 + 134x^14 - 49x^13 - 195x^12 - 375x^11 + 190x^10 + 878x^9 - 233x^8 - 491x^7 + 177x^6 + 32x^5 - 47x^4 + 21x^3 + 10x^2 - 4x - 1	\( -\,7^{14}\cdot 71^{9} \)	$C_3\times D_7$ (as 21T3)	Trivial (GRH)
21.3.142304167851792866305606535751.1	x^21 + 2x^19 - 11x^17 - 27x^16 - 82x^15 - 60x^14 - 211x^13 - 21x^12 - 494x^11 + 177x^10 - 781x^9 + 699x^8 - 1096x^7 + 966x^6 - 737x^5 + 417x^4 - 128x^3 + 18x^2 + 18x - 9	\( -\,3^{20}\cdot 151^{9} \)	21T52	Trivial (GRH)
21.3.142304167851792866305606535751.2	x^21 - 4x^19 - 2x^18 - 5x^17 + 58x^16 - 25x^15 - 201x^14 + 345x^13 - 93x^12 + 228x^11 + 426x^10 - 758x^9 - 54x^8 + 149x^7 - 473x^6 - 1772x^5 - 2981x^4 - 1405x^3 + 378x^2 + 18x - 117	\( -\,3^{20}\cdot 151^{9} \)	21T52	Trivial (GRH)
21.3.143926122875821803405026699823.1	x^21 - 12x^19 - 4x^18 + 72x^17 + 21x^16 - 261x^15 - 72x^14 + 678x^13 + 58x^12 - 1062x^11 - 285x^10 + 513x^9 + 1188x^8 - 768x^7 - 2702x^6 + 792x^5 + 1485x^4 - 865x^3 - 342x^2 + 183x - 47	\( -\,3^{28}\cdot 184607^{3} \)	21T130	Trivial (GRH)
21.3.273379262499112817938520460419.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 51x^16 - 901x^15 - 354x^14 + 2589x^13 + 1292x^12 - 4479x^11 - 2667x^10 + 4522x^9 + 3132x^8 - 2424x^7 - 2026x^6 + 438x^5 + 534x^4 - 63x^2 - 15x - 1	\( -\,23^{7}\cdot 113\cdot 710546119470924629 \)	21T162	Trivial (GRH)
21.3.378818692265664781682717625943.1	x^21 - x^14 - 2x^7 + 1	\( -\,7^{35} \)	$C_7:(C_3\times D_7)$ (as 21T16)	Trivial (GRH)
21.3.378818692265664781682717625943.2	x^21 - 4x^14 + 3x^7 + 1	\( -\,7^{35} \)	$C_7:(C_3\times D_7)$ (as 21T16)	Trivial (GRH)
21.3.378818692265664781682717625943.3	x^21 - x^14 - 9x^7 + 1	\( -\,7^{35} \)	$F_7$ (as 21T4)	Trivial (GRH)
21.3.822552053520401820057771484375.1	x^21 - 9x^20 + 39x^19 - 110x^18 + 212x^17 - 254x^16 + 72x^15 + 444x^14 - 1230x^13 + 2243x^12 - 3572x^11 + 5129x^10 - 6067x^9 + 5990x^8 - 5448x^7 + 5112x^6 - 4212x^5 + 3001x^4 - 1825x^3 + 903x^2 - 185x + 211	\( -\,5^{9}\cdot 11^{7}\cdot 43^{10} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.3.953896806899772096335364351819.1	x^21 - 5x^20 + 14x^19 - 30x^18 + 81x^17 - 198x^16 + 312x^15 - 259x^14 - 31x^13 + 395x^12 - 455x^11 + 311x^10 + 131x^9 - 101x^8 + 292x^7 + 104x^6 + 29x^5 + 133x^4 + 67x^3 + 11x^2 + 4x + 1	\( -\,3^{4}\cdot 11^{9}\cdot 13^{12}\cdot 463^{2} \)	21T98	Trivial (GRH)
21.3.1078228439505013455412874919936.1	x^21 - 6x^19 - 6x^18 + 36x^17 + 30x^16 - 138x^15 - 36x^14 + 447x^13 - 10x^12 - 1071x^11 + 888x^10 + 1111x^9 - 3042x^8 + 993x^7 + 2302x^6 - 1764x^5 + 648x^4 - 800x^3 + 864x^2 - 576x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	$[2]$ (GRH)
21.3.1078228439505013455412874919936.2	x^21 - 3x^19 - 2x^18 - 9x^17 - 12x^16 - 4x^15 + 81x^13 + 216x^12 + 459x^11 + 906x^10 + 367x^9 - 2196x^8 - 6807x^7 - 14494x^6 - 22572x^5 - 23256x^4 - 15184x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 184607^{3} \)	21T152	Trivial (GRH)
21.3.7655337671796811085236857471811.1	x^21 - 6x^20 + 19x^19 - 35x^18 + 34x^17 - 27x^16 + 33x^15 - 73x^14 + 37x^13 + 44x^12 + 137x^11 - 33x^10 + 60x^9 + 177x^8 + 243x^7 - 219x^6 - 876x^5 - 1332x^4 - 1192x^3 - 736x^2 - 288x - 64	\( -\,7^{14}\cdot 29^{3}\cdot 77351^{3} \)	21T45	Trivial (GRH)
21.3.7857627321843320792892969664512.1	x^21 + 3x^19 + 18x^17 - 54x^16 + 58x^15 - 90x^14 - 75x^13 + 288x^12 - 486x^11 + 1380x^10 - 1915x^9 + 2988x^8 - 3399x^7 + 1690x^6 - 2232x^5 - 384x^4 - 1344x^3 - 384x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 71^{9} \)	21T131	Trivial (GRH)
21.3.9785353109399805100134419972096.1	x^21 - x^20 - 10x^19 + 8x^18 + 32x^17 - 59x^16 + 7x^15 + 422x^14 + 190x^13 - 795x^12 - 1054x^11 + 695x^10 + 3497x^9 - 381x^8 - 4108x^7 + 1137x^6 + 364x^5 - 117x^4 + x^3 + 12x^2 - 3x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 184607^{3} \)	21T74	Trivial (GRH)
21.3.11238530872385902708009257189376.1	x^21 - x^20 - 3x^19 + 15x^18 - 14x^17 - 42x^16 + 112x^15 + 113x^14 + 10x^13 - 937x^12 - 860x^11 + 1848x^10 + 3892x^9 - 2944x^8 - 2961x^7 + 1339x^6 - 176x^5 - 182x^4 + 74x^3 - 4x^2 - 6x + 1	\( -\,2^{14}\cdot 37^{7}\cdot 193327^{3} \)	21T74	Trivial (GRH)
21.3.12777737809210143774260519108727.1	x^21 - 3x^14 - 6x^7 - 1	\( -\,3^{28}\cdot 7^{21} \)	21T24	Trivial (GRH)
21.3.12777737809210143774260519108727.2	x^21 - 3x^7 - 1	\( -\,3^{28}\cdot 7^{21} \)	21T24	Trivial (GRH)
21.3.12777737809210143774260519108727.3	x^21 - 9x^14 + 15x^7 + 1	\( -\,3^{28}\cdot 7^{21} \)	$C_3\times F_7$ (as 21T9)	Trivial (GRH)
21.3.86433900540276528721822666309632.1	x^21 - 2x^18 - 18x^17 + 12x^16 + 93x^15 + 252x^14 + 756x^13 + 424x^12 - 846x^11 - 3942x^10 - 12420x^9 - 20592x^8 - 30729x^7 - 35272x^6 - 30168x^5 - 18600x^4 - 8512x^3 - 2880x^2 - 768x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 11\cdot 71^{9} \)	21T131	Trivial (GRH)
21.3.140546066200987919382387150626943.1	x^21 - 6x^20 + 12x^19 + 3x^18 - 60x^17 + 108x^16 - 18x^15 - 225x^14 + 357x^13 - 89x^12 - 387x^11 + 522x^10 - 121x^9 - 312x^8 + 315x^7 - 47x^6 - 108x^5 + 75x^4 - 8x^3 - 12x^2 + 6x - 1	\( -\,3^{18}\cdot 23^{7}\cdot 10322161^{2} \)	21T156	Trivial (GRH)
21.3.160091556105803523932869333700219.1	x^21 - 3x^20 + 3x^19 - 2x^18 - 3x^17 + 11x^16 - 25x^15 + 45x^14 - 52x^13 + 43x^12 + 51x^11 - 121x^10 + 143x^9 - 83x^8 - 62x^7 + 95x^6 - 203x^5 + 45x^4 - 50x^3 - 26x^2 + 3x - 7	\( -\,11^{9}\cdot 13^{12}\cdot 37^{2}\cdot 1459^{2} \)	21T98	Trivial (GRH)
21.3.171648210515488829655228363467583.1	x^21 - 6x^20 + 12x^19 + 5x^18 - 66x^17 + 108x^16 + 6x^15 - 261x^14 + 345x^13 - 11x^12 - 453x^11 + 474x^10 - 33x^9 - 336x^8 + 279x^7 - 19x^6 - 108x^5 + 69x^4 - 6x^3 - 12x^2 + 6x - 1	\( -\,3^{18}\cdot 7^{4}\cdot 23^{7}\cdot 232801^{2} \)	21T156	Trivial (GRH)
21.3.372153638957891448013587938820096.1	x^21 + 11x^19 - 8x^18 + 72x^17 - 48x^16 + 204x^15 + 249x^13 + 376x^12 + 18x^11 + 62x^10 - 473x^9 - 1008x^8 - 975x^7 + 192x^6 - 324x^5 + 936x^4 + 368x^3 - 576x^2 - 128x + 128	\( -\,2^{14}\cdot 3^{36}\cdot 73^{6} \)	21T151	Trivial (GRH)
21.3.374031156573051227998849803993088.1	x^21 - 6x^20 + x^19 + 53x^18 - 27x^17 - 293x^16 - 9x^15 + 1527x^14 + 243x^13 - 5106x^12 - 1574x^11 + 12477x^10 + 3557x^9 - 22537x^8 + 2995x^7 + 24604x^6 - 19343x^5 - 8523x^4 + 22177x^3 - 14282x^2 + 4522x - 290	\( -\,2^{14}\cdot 7^{15}\cdot 37^{10} \)	$S_3\times F_7$ (as 21T15)	Trivial (GRH)
21.3.837604276918124655203492919754752.1	x^21 - 6x^20 + 13x^19 - 17x^18 + 21x^17 - 45x^16 + 82x^15 - 15x^14 + 21x^13 - 84x^12 + 93x^11 + 37x^10 - 137x^9 - 497x^8 - 444x^7 - 317x^6 - 346x^5 - 656x^4 - 808x^3 - 640x^2 - 288x - 64	\( -\,2^{14}\cdot 3^{7}\cdot 13^{3}\cdot 31^{3}\cdot 47^{7}\cdot 89^{3} \)	21T62	Trivial (GRH)
21.3.868742059496237220358847069077504.1	x^21 - x^14 - 3x^7 + 1	\( -\,2^{14}\cdot 7^{21}\cdot 37^{7} \)	21T29	Trivial (GRH)