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 19635)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1999004627104432128.1	x^18 - 6x^17 + 24x^16 - 68x^15 + 159x^14 - 300x^13 + 479x^12 - 630x^11 + 702x^10 - 636x^9 + 480x^8 - 270x^7 + 114x^6 - 12x^5 - 12x^4 + 14x^3 - 3x^2 + 1	\( -\,2^{18}\cdot 3^{27} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.9651146816936671875.1	x^18 - 9x^17 + 36x^16 - 78x^15 + 84x^14 - 111x^12 + 90x^11 + 72x^10 - 156x^9 + 45x^8 + 81x^7 - 57x^6 - 27x^5 + 36x^4 - 9x^2 + 3	\( -\,3^{31}\cdot 5^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.13509211106101054707.1	x^18 - 6x^17 + 9x^16 + 14x^15 - 42x^14 - 21x^13 + 131x^12 - 51x^11 - 162x^10 + 126x^9 + 108x^8 - 138x^7 - 18x^6 + 84x^5 - 33x^4 - 11x^3 + 15x^2 - 6x + 1	\( -\,3^{27}\cdot 11^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.14176142707705638912.1	x^18 - 7x^17 + 29x^16 - 86x^15 + 204x^14 - 403x^13 + 684x^12 - 1007x^11 + 1301x^10 - 1479x^9 + 1488x^8 - 1316x^7 + 1016x^6 - 673x^5 + 378x^4 - 171x^3 + 58x^2 - 10x + 1	\( -\,2^{12}\cdot 3^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.56693912375296000000.1	x^18 - 6x^17 + 21x^16 - 54x^15 + 116x^14 - 226x^13 + 412x^12 - 686x^11 + 997x^10 - 1220x^9 + 1225x^8 - 994x^7 + 652x^6 - 356x^5 + 169x^4 - 70x^3 + 25x^2 - 6x + 1	\( -\,2^{18}\cdot 5^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.71418001746108874752.2	x^18 - 11x^15 + 48x^12 - 49x^9 + 48x^6 - 11x^3 + 1	\( -\,2^{18}\cdot 3^{9}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.110730297608000000000.1	x^18 - 5x^17 + 5x^16 + 10x^15 - 19x^14 + 7x^13 - 18x^12 + 34x^11 + 21x^10 - 70x^9 + 22x^8 + 14x^7 + 11x^6 - 7x^5 - 20x^4 + 13x^3 - x^2 + 4x - 1	\( 2^{12}\cdot 5^{9}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.161919374795459002368.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 417x^14 - 903x^13 + 1635x^12 - 2517x^11 + 3336x^10 - 3832x^9 + 3861x^8 - 3447x^7 + 2793x^6 - 2067x^5 + 1401x^4 - 819x^3 + 381x^2 - 120x + 19	\( -\,2^{18}\cdot 3^{31} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.169287115250035851264.1	x^18 + 6x^16 + 15x^14 + 11x^12 - 21x^10 - 48x^8 - 8x^6 + 45x^4 + 27x^2 + 1	\( -\,2^{24}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.209657417785715740672.1	x^18 - 5x^17 + 9x^16 - 6x^15 - 5x^14 + 16x^13 - 14x^12 + 13x^11 - 33x^10 + 54x^9 - 59x^8 + 34x^7 - 12x^6 + 35x^5 - 39x^4 + 8x^3 - 3x^2 + 6x - 1	\( 2^{12}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.303256405652583481344.2	x^18 + 9x^16 + 36x^14 + 97x^12 + 171x^10 + 189x^8 + 131x^6 + 54x^4 + 12x^2 + 1	\( -\,2^{30}\cdot 3^{24} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.303843936636352000000.1	x^18 - 7x^17 + 26x^16 - 71x^15 + 151x^14 - 255x^13 + 343x^12 - 341x^11 + 206x^10 - 4x^9 - 127x^8 + 82x^7 + 55x^6 - 93x^5 + 34x^4 + 19x^3 - 10x^2 - 2x + 1	\( -\,2^{12}\cdot 5^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.303843936636352000000.2	x^18 - 3x^17 + 7x^16 - 12x^15 + 20x^14 - 29x^13 + 39x^12 - 59x^11 + 96x^10 - 151x^9 + 210x^8 - 264x^7 + 290x^6 - 272x^5 + 216x^4 - 144x^3 + 80x^2 - 32x + 8	\( -\,2^{12}\cdot 5^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.382755853108052250624.1	x^18 - 4x^17 + 5x^16 - x^15 - 7x^14 + 19x^13 - 23x^12 + 27x^11 - 15x^10 - 40x^9 + 42x^8 + 3x^7 + 15x^6 - 23x^5 - 11x^4 + 20x^3 - 7x^2 - x + 1	\( 2^{12}\cdot 3^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.488038239039168000000.1	x^18 - 3x^17 + 6x^16 - 15x^15 + 21x^14 - 33x^13 + 73x^12 - 123x^11 + 216x^10 - 257x^9 + 72x^8 + 171x^7 - 164x^6 - 12x^5 + 72x^4 - 19x^3 - 9x^2 + 3x + 1	\( -\,2^{12}\cdot 3^{27}\cdot 5^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.907273133293160890368.1	x^18 - 6x^17 + 17x^16 - 36x^15 + 76x^14 - 140x^13 + 228x^12 - 348x^11 + 465x^10 - 542x^9 + 551x^8 - 488x^7 + 373x^6 - 234x^5 + 127x^4 - 52x^3 + 17x^2 - 2x + 1	\( -\,2^{18}\cdot 3^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.1023490369077469249536.1	x^18 - 8x^15 - 12x^14 - 12x^13 - 6x^12 + 24x^11 + 18x^10 + 42x^9 - 6x^8 - 55x^6 - 6x^4 + 2x^3 + 30x^2 - 12x + 1	\( 2^{27}\cdot 3^{27} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.1156831381426176000000.1	x^18 - 6x^17 + 21x^16 - 50x^15 + 93x^14 - 144x^13 + 186x^12 - 210x^11 + 201x^10 - 118x^9 + 51x^8 + 30x^7 - 24x^6 + 18x^5 + 12x^4 - 18x^3 + 15x^2 - 6x + 1	\( -\,2^{18}\cdot 3^{24}\cdot 5^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.1354296922000286810112.1	x^18 - 6x^17 + 19x^16 - 36x^15 + 31x^14 + 32x^13 - 161x^12 + 318x^11 - 419x^10 + 376x^9 - 234x^8 + 78x^7 + 45x^6 - 60x^5 + 23x^4 - 4x^3 - 5x^2 + 2x + 1	\( 2^{27}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.1839302601739695422127.2	x^18 - 6x^15 + 15x^12 - 20x^9 + 22x^6 - 6x^3 + 1	\( -\,3^{18}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.1878328153971890270208.2	x^18 - x^17 + 3x^16 + 4x^15 - 2x^14 + 13x^13 + 2x^12 + 6x^11 + 10x^10 - 9x^9 + 19x^8 - 25x^7 + 15x^6 - 19x^5 + 15x^4 - 6x^3 + 6x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{9}\cdot 13^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.2259436291848000000000.1	x^18 - 6x^17 + 15x^16 - 12x^15 - 39x^14 + 153x^13 - 265x^12 + 243x^11 + 9x^10 - 417x^9 + 768x^8 - 906x^7 + 751x^6 - 372x^5 + 66x^4 + 19x^3 - 9x^2 + 3x - 1	\( 2^{12}\cdot 3^{24}\cdot 5^{9} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.2426051245220667850752.2	x^18 - 3x^14 + 20x^12 - 6x^10 - 60x^8 + 73x^6 - 42x^4 + 24x^2 - 8	\( 2^{33}\cdot 3^{24} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.3454279995636458717184.2	x^18 - 9x^16 + 33x^14 - 24x^12 - 36x^10 + 75x^8 - 21x^6 - 9x^4 + 6x^2 + 1	\( -\,2^{24}\cdot 3^{30} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.4570752111750967984128.2	x^18 - 6x^16 + 7x^14 + 11x^12 - 17x^10 - 8x^8 + 16x^6 - 75x^4 + 99x^2 - 27	\( 2^{24}\cdot 3^{9}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.5425784582792000000000.1	x^18 - 5x^17 + 9x^16 - 6x^15 - 19x^14 + 71x^13 - 117x^12 + 135x^11 - 70x^10 - 84x^9 + 177x^8 - 123x^7 - 51x^6 + 135x^5 - 33x^4 - 25x^3 + 11x^2 - 8x + 1	\( 2^{12}\cdot 5^{9}\cdot 7^{14} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.6.8187922952619753996288.1	x^18 - 3x^16 - 15x^12 - 9x^10 - 27x^8 + 27x^6 + 54x^4 - 27	\( 2^{30}\cdot 3^{27} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.10362839986909376151552.1	x^18 - 9x^16 + 33x^14 - 60x^12 + 72x^10 - 81x^8 + 75x^6 - 45x^4 + 18x^2 - 3	\( 2^{24}\cdot 3^{31} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.10834375376002294480896.3	x^18 + 8x^16 + 18x^14 + 27x^12 + 45x^10 + 7x^8 + x^6 - 8x^4 + 13x^2 + 1	\( -\,2^{30}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.11067041604778727959971.1	x^18 - 7x^17 + 24x^16 - 63x^15 + 140x^14 - 266x^13 + 466x^12 - 738x^11 + 1061x^10 - 1410x^9 + 1756x^8 - 1965x^7 + 1884x^6 - 1470x^5 + 891x^4 - 390x^3 + 112x^2 - 16x + 1	\( -\,3^{6}\cdot 19^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
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)	$[2]$
18.6.13418074738285807403008.1	x^18 - x^17 + x^16 + 3x^15 - 24x^14 - 16x^13 - 67x^12 - 74x^11 - 48x^10 - 49x^9 + 261x^8 + 283x^7 + 457x^6 + 225x^5 + 125x^4 + 16x^3 - 3x^2 + 4x - 1	\( 2^{18}\cdot 13^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.0.17436035582546112000000.1	x^18 + x^16 - 6x^15 - 4x^14 - 5x^13 - 6x^12 + 16x^11 + 22x^10 + 43x^9 + 41x^8 - 34x^7 + 121x^6 - 49x^5 + 17x^4 + 15x^3 - 4x^2 - x + 1	\( -\,2^{12}\cdot 3^{9}\cdot 5^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.17513643935890567069696.1	x^18 - 8x^15 + 21x^14 - 28x^13 + 32x^12 - 70x^11 + 182x^10 - 290x^9 + 280x^8 - 140x^7 + x^6 + 42x^5 - 14x^4 - 4x^3 + 8	\( -\,2^{18}\cdot 7^{12}\cdot 13^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.17980759982220503815017.1	x^18 - 10x^15 - 12x^14 + 3x^13 + 12x^12 + 75x^11 + 18x^10 + 48x^9 - 69x^8 + 54x^7 - 145x^6 + 189x^5 - 195x^4 + 169x^3 - 114x^2 + 48x - 8	\( 3^{27}\cdot 11^{9} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.19446011944726528000000.1	x^18 - 6x^17 + 11x^16 + 6x^15 - 60x^14 + 122x^13 - 141x^12 + 74x^11 + 54x^10 - 122x^9 + 71x^8 + 36x^7 - 70x^6 + 16x^5 + 33x^4 - 10x^3 - 11x^2 - 4x + 1	\( 2^{18}\cdot 5^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.20697725611846923828125.1	x^18 - x^17 - 9x^16 + 6x^15 + 20x^14 + 44x^13 - 84x^12 - 111x^11 + 29x^10 + 115x^9 + 121x^8 + 109x^7 + 56x^6 + 11x^5 - 25x^4 - 29x^3 - 11x^2 - 4x + 1	\( 5^{15}\cdot 7^{14} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.24496374598915344039936.1	x^18 + 2x^16 - 5x^15 - 3x^14 + 22x^13 - 23x^12 + 45x^11 + 117x^10 - 54x^9 - 54x^8 - 21x^7 + 15x^6 + 39x^5 - 63x^4 + 17x^3 + 15x^2 - 8x + 1	\( 2^{18}\cdot 3^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.27634239965091669737472.1	x^18 - 6x^16 + 6x^14 - 6x^13 - 24x^12 - 6x^11 + 99x^10 + 160x^9 + 39x^8 - 210x^7 - 372x^6 - 246x^5 + 9x^4 + 96x^3 + 24x^2 - 12x - 1	\( 2^{27}\cdot 3^{30} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.6.31234447298506752000000.1	x^18 - 6x^17 + 15x^16 - 26x^15 + 45x^14 - 54x^13 - 48x^12 + 390x^11 - 912x^10 + 1260x^9 - 1077x^8 + 420x^7 + 251x^6 - 534x^5 + 435x^4 - 214x^3 + 66x^2 - 12x + 1	\( 2^{18}\cdot 3^{27}\cdot 5^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.34449796366811672670208.1	x^18 - x^17 + 2x^15 - 3x^14 + x^13 + 4x^12 + 7x^11 - 10x^10 + 7x^9 + 10x^8 - 27x^7 + 24x^6 + 13x^5 + 7x^4 + 4x^3 + 2x^2 + x + 1	\( -\,2^{12}\cdot 7^{15}\cdot 11^{6} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
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)	$[2]$
18.6.49661170246971776397429.2	x^18 - 9x^17 + 30x^16 - 29x^15 - 105x^14 + 462x^13 - 867x^12 + 819x^11 - 114x^10 - 585x^9 + 579x^8 - 126x^7 - 139x^6 + 105x^5 - 43x^3 + 30x^2 - 9x + 1	\( 3^{21}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.6.58065480530762296983552.1	x^18 - 4x^17 + 4x^16 - 20x^15 + 51x^14 + 24x^13 + 3x^12 - 162x^11 - 195x^10 + 90x^9 + 324x^8 + 372x^7 - 74x^6 - 184x^5 - 215x^4 - 28x^3 - 25x^2 + 10x + 1	\( 2^{24}\cdot 3^{6}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
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)	$[2]$
18.6.80722386956232000000000.1	x^18 - 9x^16 - 4x^15 + 30x^14 + 25x^13 + 44x^12 - 50x^11 - 304x^10 + 131x^9 + 295x^8 - 162x^7 - 65x^6 + 69x^5 - 75x^4 + 11x^3 + 28x^2 - 5x - 1	\( 2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)
18.0.86675003008018355847168.1	x^18 + 20x^12 + 68x^6 + 8	\( -\,2^{33}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.0.86675003008018355847168.2	x^18 - 4x^17 + 6x^16 - 18x^15 + 54x^14 - 74x^13 + 135x^12 - 274x^11 + 151x^10 + 98x^9 - 31x^8 + 20x^7 + 29x^6 - 16x^5 + 6x^4 + 18x^3 + 13x^2 - 2x + 1	\( -\,2^{33}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial
18.6.86675003008018355847168.2	x^18 - 20x^12 + 68x^6 - 8	\( 2^{33}\cdot 3^{6}\cdot 7^{12} \)	$S_3 \times C_6$ (as 18T6)	Trivial (GRH)