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 )

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1206393352117083984375.1	x^18 - 6x^17 + 21x^16 - 51x^15 + 87x^14 - 102x^13 + 48x^12 + 90x^11 - 234x^10 + 298x^9 - 156x^8 - 120x^7 + 354x^6 - 384x^5 + 273x^4 - 132x^3 + 45x^2 - 9x + 1	\( -\,3^{31}\cdot 5^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.2279403313291670831424.1	x^18 - 3x^17 + 6x^16 - 20x^15 + 57x^14 - 102x^13 + 159x^12 - 312x^11 + 567x^10 - 735x^9 + 855x^8 - 1155x^7 + 1382x^6 - 1122x^5 + 567x^4 - 172x^3 + 33x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{21}\cdot 23^{7} \)	18T734	$[2]$ (GRH)
18.0.6342687480463779704832.4	x^18 - 6x^16 + 21x^14 - 45x^12 + 63x^10 - 36x^8 - 27x^6 + 81x^4 - 54x^2 + 27	\( -\,2^{12}\cdot 3^{21}\cdot 23^{6} \)	18T518	$[2]$
18.0.6778308875544000000000.1	x^18 - 3x^17 + 9x^16 - 12x^15 + 30x^14 - 15x^13 + 36x^12 - 27x^11 + 45x^10 - 69x^9 + 126x^8 - 162x^7 + 144x^6 - 117x^5 + 72x^4 - 27x^3 + 9	\( -\,2^{12}\cdot 3^{25}\cdot 5^{9} \)	$S_3^2$ (as 18T11)	$[2]$
18.0.7086739046912000000000.1	x^18 - 6x^17 + 28x^16 - 102x^15 + 296x^14 - 696x^13 + 1429x^12 - 2684x^11 + 4639x^10 - 7178x^9 + 9523x^8 - 10268x^7 + 8521x^6 - 5202x^5 + 2254x^4 - 672x^3 + 133x^2 - 16x + 1	\( -\,2^{18}\cdot 5^{9}\cdot 7^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.7278153735662003552256.1	x^18 + 3x^14 + 24x^12 + 3x^10 - 66x^8 - 27x^6 + 36x^4 + 36x^2 + 6	\( -\,2^{33}\cdot 3^{25} \)	$S_3^2$ (as 18T11)	$[2]$
18.0.10460353203000000000000.1	x^18 + 49x^12 + 67x^6 + 27	\( -\,2^{12}\cdot 3^{21}\cdot 5^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[3]$
18.0.11727564985436483639043.1	x^18 - 3x^16 - 6x^15 + 6x^14 + 15x^13 - 6x^12 - 24x^11 - 3x^10 + 43x^9 + 54x^8 - 24x^7 - 12x^6 - 42x^5 + 12x^4 + 15x^3 + 6x^2 + 3x + 1	\( -\,3^{25}\cdot 7^{12} \)	$He_3:C_2$ (as 18T21)	$[3]$
18.0.13418074738285807403008.1	x^18 + 10x^16 - 2x^15 + 46x^14 - 8x^13 + 75x^12 + 34x^11 - 7x^10 + 80x^9 + 8x^8 - 34x^7 + 209x^6 - 32x^5 - 42x^4 + 30x^3 + 11x^2 - 4x + 1	\( -\,2^{18}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.18283008447003871936512.1	x^18 - x^17 - 3x^16 + 8x^15 - 4x^13 + 40x^12 - 74x^11 - 3x^10 + 299x^9 - 181x^8 - 158x^7 + 506x^6 + 166x^5 + 86x^4 + 36x^3 + 9x^2 + x + 1	\( -\,2^{26}\cdot 3^{9}\cdot 7^{12} \)	$S_3^2$ (as 18T11)	$[3]$
18.0.22174929740517389369344.1	x^18 - x^16 - 4x^14 - 4x^12 + 30x^10 + 26x^8 - 72x^6 - 40x^4 + 61x^2 + 19	\( -\,2^{36}\cdot 19^{9} \)	18T185	$[2]$
18.0.22367896927548830134272.2	x^18 - 6x^16 + 25x^14 - 61x^12 + 127x^10 - 170x^8 + 190x^6 - 114x^4 + 45x^2 + 27	\( -\,2^{12}\cdot 3^{9}\cdot 23^{6}\cdot 37^{4} \)	18T775	$[2]$ (GRH)
18.0.23465261991844685929951.1	x^18 - 6x^17 + 19x^16 - 34x^15 + 42x^14 - 34x^13 + 20x^12 + 20x^11 - 97x^10 + 148x^9 - 131x^8 - 30x^7 + 251x^6 - 76x^5 - 53x^4 + 8x^3 + 11x^2 + 4x + 1	\( -\,31^{15} \)	$S_3 \times C_3$ (as 18T3)	$[3]$
18.0.24930271280154907835063.1	x^18 - 3x^17 + 7x^16 - 8x^15 + 35x^14 - 28x^13 + 110x^12 - 162x^11 + 286x^10 - 260x^9 + 262x^8 - 100x^7 + 124x^6 - 126x^5 + 105x^4 - 43x^3 + 21x^2 - 6x + 1	\( -\,7^{12}\cdot 23^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3]$
18.0.36566016894007743873024.1	x^18 + 2x^16 - 6x^14 - 30x^12 - 19x^10 + 292x^8 + 337x^6 + 66x^4 + 540x^2 + 216	\( -\,2^{27}\cdot 3^{9}\cdot 7^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.37980492079544000000000.1	x^18 - 6x^17 + 26x^16 - 79x^15 + 210x^14 - 448x^13 + 876x^12 - 1414x^11 + 2146x^10 - 2653x^9 + 3166x^8 - 2968x^7 + 2738x^6 - 1960x^5 + 1344x^4 - 753x^3 + 318x^2 - 34x + 71	\( -\,2^{12}\cdot 5^{9}\cdot 7^{15} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.37980492079544000000000.2	x^18 + x^16 - 16x^15 + 8x^14 - 53x^13 + 110x^12 - 62x^11 + 188x^10 - 65x^9 + 109x^8 - 70x^7 + 57x^6 - 71x^5 + 49x^4 - 31x^3 + 16x^2 - 3x + 1	\( -\,2^{12}\cdot 5^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.40310784000000000000000.1	x^18 - 7x^17 + 20x^16 - 22x^15 - 20x^14 + 88x^13 - 86x^12 - 40x^11 + 149x^10 - 65x^9 - 60x^8 + 60x^7 + 70x^6 - 10x^4 + 38x^3 + 44x^2 + 20x + 4	\( -\,2^{26}\cdot 3^{9}\cdot 5^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[2]$ (GRH)
18.0.41451359947637504606208.2	x^18 - 9x^17 + 33x^16 - 60x^15 + 60x^14 - 84x^13 + 222x^12 - 318x^11 + 153x^10 + 5x^9 + 153x^8 - 318x^7 + 222x^6 - 84x^5 + 60x^4 - 60x^3 + 33x^2 - 9x + 1	\( -\,2^{26}\cdot 3^{31} \)	$S_3^2$ (as 18T11)	$[3]$
18.0.52301766015000000000000.1	x^18 + 9x^16 - x^15 + 27x^14 - 6x^13 + 46x^12 - 27x^11 + 123x^10 - 83x^9 + 234x^8 - 54x^7 + 118x^6 + 48x^5 + 132x^4 + 108x^3 + 336x^2 + 264x + 184	\( -\,2^{12}\cdot 3^{21}\cdot 5^{13} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$
18.0.53137762492763568359375.1	x^18 - 4x^16 - 6x^14 + 64x^12 - 145x^10 + 279x^8 - 446x^6 + 206x^4 + 341x^2 + 335	\( -\,5^{9}\cdot 67^{9} \)	$D_9$ (as 18T5)	$[2]$
18.0.54949782158942378487808.1	x^18 - 3x^17 + 13x^16 - 34x^15 + 89x^14 - 168x^13 + 310x^12 - 492x^11 + 672x^10 - 786x^9 + 1036x^8 - 1044x^7 + 928x^6 - 576x^5 + 379x^4 - 153x^3 + 51x^2 + 8x + 1	\( -\,2^{12}\cdot 7^{15}\cdot 41^{4} \)	18T201	$[3]$
18.0.61004779879896000000000.1	x^18 + 12x^16 - 6x^15 + 54x^14 - 42x^13 + 109x^12 - 90x^11 + 45x^10 - 32x^9 - 99x^8 + 30x^7 - 17x^6 + 30x^4 + 8x^3 + 9x^2 + 6x + 1	\( -\,2^{12}\cdot 3^{27}\cdot 5^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.65503383620958031970304.1	x^18 + 6x^16 + 27x^14 + 48x^12 + 27x^10 + 54x^8 - 315x^6 - 324x^4 + 324x^2 + 216	\( -\,2^{33}\cdot 3^{27} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.77209174535493375000000.1	x^18 - 9x^12 - 27x^9 + 324x^6 + 324x^3 + 216	\( -\,2^{6}\cdot 3^{31}\cdot 5^{9} \)	$C_3^3:C_2^2$ (as 18T53)	$[2]$
18.0.81721509398437500000000.1	x^18 - 6x^17 + 18x^16 - 34x^15 + 45x^14 - 66x^13 + 176x^12 - 498x^11 + 1104x^10 - 1890x^9 + 2523x^8 - 2628x^7 + 2139x^6 - 1362x^5 + 675x^4 - 254x^3 + 69x^2 - 12x + 1	\( -\,2^{8}\cdot 3^{21}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2]$
18.0.82902719895275009212416.1	x^18 + 6x^16 - 12x^15 + 21x^14 - 72x^13 + 144x^12 - 282x^11 + 462x^10 - 620x^9 + 864x^8 - 1122x^7 + 1206x^6 - 948x^5 + 549x^4 - 228x^3 + 66x^2 - 12x + 1	\( -\,2^{27}\cdot 3^{31} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.83769291871618924818432.1	x^18 - 3x^17 + 3x^16 + 9x^14 - 45x^13 + 102x^12 - 105x^11 + 123x^10 - 110x^9 + 147x^8 - 183x^7 + 207x^6 - 198x^5 + 144x^4 - 120x^3 + 96x^2 - 96x + 64	\( -\,2^{12}\cdot 3^{25}\cdot 17^{6} \)	$S_3^2$ (as 18T11)	$[3]$
18.0.86221016299768945573888.1	x^18 + 5x^16 + 10x^14 + 16x^12 + 29x^10 + 61x^8 + 89x^6 + 65x^4 + 39x^2 + 13	\( -\,2^{24}\cdot 7^{12}\cdot 13^{5} \)	18T282	$[2]$
18.0.90466292782051905202183.1	x^18 - 2x^17 + 4x^16 + 5x^15 + 13x^14 - 16x^13 + 41x^12 - 37x^11 + 69x^10 - 186x^9 + 472x^8 - 593x^7 + 672x^6 - 521x^5 + 389x^4 - 176x^3 + 75x^2 - 14x + 1	\( -\,7^{15}\cdot 138041^{2} \)	18T286	$[2]$
18.2.92225142947365783203125.1	x^18 + 2x^16 - 3x^15 - 14x^14 + 18x^13 - 79x^12 + 154x^11 - 297x^10 + 475x^9 - 701x^8 + 794x^7 - 869x^6 + 586x^5 - 428x^4 + 108x^3 + 54x^2 - 23x - 19	\( 5^{9}\cdot 241^{7} \)	18T626	$[2]$
18.0.93265559882184385363968.1	x^18 - 3x^17 + 6x^16 - 3x^15 - 3x^14 + 6x^13 - 9x^12 + 15x^11 - 39x^10 - 2x^9 + 48x^8 - 42x^7 + 3x^6 + 21x^5 + 39x^4 + 18x^3 + 3x^2 + 3x + 1	\( -\,2^{24}\cdot 3^{33} \)	$C_2\times He_3:C_2$ (as 18T41)	$[3]$
18.0.96412994581196722733056.1	x^18 + 10x^16 + 38x^14 + 66x^12 + 46x^10 + 7x^8 + 23x^6 + 44x^4 + 24x^2 + 4	\( -\,2^{16}\cdot 101^{2}\cdot 229^{6} \)	18T556	$[2]$
18.2.99714188227072000000000.1	x^18 - 4x^17 - 3x^16 + 28x^15 - 11x^14 - 62x^13 + 40x^12 + 42x^11 - 22x^10 + 26x^9 - 9x^8 - 16x^7 - 73x^6 - 154x^5 - 29x^4 - 2x^3 - 44x^2 - 8x - 1	\( 2^{18}\cdot 5^{9}\cdot 41^{7} \)	18T273	$[2]$
18.0.105192903852687811100983.1	x^18 - 4x^17 + 6x^16 - 3x^15 + 7x^14 - 28x^13 + 43x^12 - 28x^11 + 11x^10 - 33x^8 + 70x^7 - 55x^6 - 14x^5 + 70x^4 - 68x^3 + 34x^2 - 9x + 1	\( -\,7^{15}\cdot 43^{4}\cdot 6481 \)	18T766	$[2]$
18.0.105226667788517176205647.1	x^18 - 6x^17 + 17x^16 - 26x^15 + 40x^14 - 98x^13 + 214x^12 - 180x^11 + 94x^10 + 240x^9 - 166x^8 - 346x^7 + 387x^6 + 144x^5 + 183x^4 + 45x^3 + 21x^2 + 3x + 1	\( -\,7^{15}\cdot 53^{6} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.118039224225889612726272.1	x^18 - 12x^15 - 18x^14 + 51x^12 + 72x^11 + 72x^10 + 36x^9 + 72x^8 + 90x^7 + 75x^6 + 72x^5 + 54x^4 - 18x^2 + 3	\( -\,2^{18}\cdot 3^{37} \)	$C_3:S_4$ (as 18T40)	$[2]$
18.0.119087320609277524873216.1	x^18 + 9x^16 + 37x^14 + 93x^12 + 158x^10 + 187x^8 + 149x^6 + 69x^4 + 15x^2 + 1	\( -\,2^{12}\cdot 229^{6}\cdot 449^{2} \)	18T556	$[2]$
18.0.120334583646716719921875.1	x^18 - 2x^17 + 4x^16 + 2x^15 - 2x^14 + 6x^13 + 15x^12 - 4x^11 + 17x^10 + 10x^9 + 32x^8 + 9x^7 + 15x^6 + 34x^5 + 13x^4 + 8x^3 + 7x^2 + 3x + 1	\( -\,3^{17}\cdot 5^{8}\cdot 13^{4}\cdot 17^{4} \)	18T888	$[2]$
18.0.144603922678272000000000.1	x^18 - 3x^16 - 6x^14 + 33x^10 + 273x^8 - 19x^6 + 225x^4 + 675x^2 + 125	\( -\,2^{18}\cdot 3^{24}\cdot 5^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2]$
18.0.144884079282928466796875.1	x^18 - 5x^17 + 6x^16 - x^15 + 25x^14 - 75x^13 + 50x^12 - 15x^11 + 155x^10 - 220x^9 + 111x^8 - 60x^7 + 146x^6 - 56x^5 + 50x^4 - 51x^3 + 40x^2 - 11x + 1	\( -\,5^{15}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2]$
18.0.145340952056670741069824.1	x^18 + 2x^16 - 4x^14 + x^12 + 24x^10 + 100x^8 - 13x^6 + 50x^4 + 76x^2 + 59	\( -\,2^{24}\cdot 59^{9} \)	$C_2^2:D_9$ (as 18T39)	$[2]$
18.0.151749870875069854858407.1	x^18 - 3x^17 - 3x^16 + 20x^15 + 9x^14 - 60x^13 - 63x^12 + 60x^11 + 345x^10 - 40x^9 - 237x^8 - 489x^7 + 136x^6 + 129x^5 + 63x^4 + 102x^3 + 168x^2 + 87	\( -\,3^{21}\cdot 29^{9} \)	$D_9$ (as 18T5)	$[2]$
18.0.173153579917474218640896.1	x^18 + 5x^16 + 7x^14 - 4x^13 - 5x^12 - 27x^11 - 19x^10 - 22x^9 + 44x^8 + 92x^7 + 212x^6 + 351x^5 + 481x^4 + 385x^3 + 168x^2 + 23x + 1	\( -\,2^{9}\cdot 3^{9}\cdot 107^{8} \)	$C_2\times S_3\times S_4$ (as 18T111)	$[2]$
18.0.191102976000000000000000.1	x^18 - 4x^17 + 14x^15 - 24x^13 - 19x^12 + 20x^11 + 44x^10 + 20x^9 - 70x^8 - 20x^7 + 155x^6 - 100x^5 + 20x^4 + 14x^3 - 6x^2 + 1	\( -\,2^{33}\cdot 3^{6}\cdot 5^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[2]$
18.0.221502229807900608000000.1	x^18 - 4x^17 + 12x^16 - 26x^15 + 60x^14 - 92x^13 + 147x^12 - 192x^11 + 244x^10 - 236x^9 + 244x^8 - 192x^7 + 147x^6 - 92x^5 + 60x^4 - 26x^3 + 12x^2 - 4x + 1	\( -\,2^{12}\cdot 3^{6}\cdot 5^{6}\cdot 7^{15} \)	$C_2\times S_3^2$ (as 18T29)	$[3]$
18.0.230545359816190649856000.1	x^18 - 9x^15 + 36x^13 + 45x^12 - 234x^10 - 225x^9 + 252x^8 + 630x^7 + 498x^6 - 756x^5 - 1224x^4 + 252x^3 + 792x^2 + 216x + 24	\( -\,2^{12}\cdot 3^{37}\cdot 5^{3} \)	$C_2\times C_3:S_4$ (as 18T66)	$[2]$
18.2.254331344722610381338249.1	x^18 - 4x^17 + 5x^16 + 3x^15 - 9x^14 + 22x^13 - 62x^12 - 28x^11 + 432x^10 - 597x^9 - 260x^8 + 1372x^7 - 1186x^6 - 537x^5 + 1524x^4 - 829x^3 - 326x^2 + 565x - 211	\( 23^{8}\cdot 59^{3}\cdot 251^{3} \)	18T779	$[2]$ (GRH)
18.0.259979518176473365480584.1	x^18 - 9x^15 + 9x^14 + 54x^12 - 135x^11 + 81x^10 - 6x^9 + 243x^8 - 729x^7 + 999x^6 - 756x^5 + 243x^4 + 81x^3 - 81x^2 + 9	\( -\,2^{3}\cdot 3^{45}\cdot 11 \)	18T658	$[2]$
18.0.263584455435142225920000.1	x^18 + 2x^16 - 12x^14 - 36x^12 + 5x^10 + 130x^8 + 223x^6 + 201x^4 + 99x^2 + 27	\( -\,2^{16}\cdot 3^{9}\cdot 5^{4}\cdot 83^{6} \)	18T310	$[2]$

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