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 all 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.3384449153178974138944.1	x^18 - x^16 - 7x^14 + 19x^12 + 5x^10 - 42x^8 - 11x^6 + 19x^4 + 9x^2 + 1	\( -\,2^{6}\cdot 7^{12}\cdot 113^{2}\cdot 547^{2} \)	18T768	Trivial
18.0.7101528447669869215744.1	x^18 + 4x^16 + 3x^14 - 3x^12 + 4x^10 + 12x^8 - x^6 + x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T768	Trivial (GRH)
18.0.7101528447669869215744.2	x^18 + 3x^16 + 2x^14 + 4x^12 + 14x^10 + 9x^8 - x^6 + 5x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T768	Trivial
18.0.57388858189268996325376.1	x^18 - 3x^16 + 4x^14 + 9x^12 - 11x^10 + x^8 + 32x^6 + 28x^4 + 9x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T768	Trivial (GRH)
18.0.57388858189268996325376.2	x^18 + 7x^16 + 21x^14 + 41x^12 + 49x^10 + 28x^8 + 12x^6 + 14x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T768	Trivial (GRH)
18.4.57388858189268996325376.4	x^18 - 5x^16 + 5x^14 + 13x^12 - 31x^10 + 16x^8 + 8x^6 - 10x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T768	Trivial (GRH)
18.4.57388858189268996325376.5	x^18 - 3x^16 - 4x^14 + 18x^12 - 3x^10 - 23x^8 + 6x^6 + 8x^4 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T768	Trivial (GRH)
18.6.63646755821921716928512.1	x^18 - x^16 - x^14 + 5x^12 - 19x^10 - 32x^8 + 41x^6 + 70x^4 + 14x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 1583^{2} \)	18T768	Trivial (GRH)
18.6.63646755821921716928512.2	x^18 + 2x^16 + 7x^14 - 2x^12 + 7x^10 - 20x^8 - 8x^6 + 7x^4 + 14x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 1583^{2} \)	18T768	Trivial (GRH)
18.12.90466292782051905202183.1	x^18 - 7x^17 + 9x^16 + 44x^15 - 129x^14 - 27x^13 + 439x^12 - 291x^11 - 576x^10 + 632x^9 + 345x^8 - 462x^7 - 230x^6 + 207x^5 + 126x^4 - 60x^3 - 27x^2 + 6x + 1	\( -\,7^{15}\cdot 138041^{2} \)	18T768	Trivial (GRH)
18.12.136329432645150668523607.1	x^18 - 8x^17 + 19x^16 - 45x^14 + 6x^13 + 59x^12 + 58x^11 - 104x^10 - 155x^9 + 212x^8 + 122x^7 - 270x^6 + 20x^5 + 169x^4 - 62x^3 - 41x^2 + 19x + 1	\( -\,7^{15}\cdot 169457^{2} \)	18T768	Trivial (GRH)
18.8.173017860931893910933504.1	x^18 - 4x^16 + 4x^14 + x^12 - 12x^10 + 18x^8 + 6x^6 - 16x^4 + 2x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 55243^{2} \)	18T768	Trivial (GRH)
18.6.199803395729731379254417.2	x^18 - x^17 - 3x^16 + 3x^15 - 16x^14 - 7x^13 + 49x^12 + 63x^11 + 8x^10 - 100x^9 - 33x^8 + 77x^7 - 72x^6 - 107x^5 + 22x^4 + 2x^3 - 46x^2 - 20x - 1	\( 7^{12}\cdot 41^{2}\cdot 97^{5} \)	18T768	Trivial (GRH)
18.6.3362743574756719665610752.1	x^18 - 3x^16 - 27x^14 - 33x^12 + 45x^10 + 108x^8 + 81x^6 + 54x^4 - 27	\( 2^{18}\cdot 3^{27}\cdot 1297^{2} \)	18T768	Trivial (GRH)
18.10.3362743574756719665610752.2	x^18 - 3x^16 + 9x^14 - 42x^12 + 81x^10 - 135x^8 + 279x^6 - 324x^4 + 162x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 1297^{2} \)	18T768	Trivial (GRH)
18.10.3362743574756719665610752.3	x^18 - 12x^16 + 36x^14 + 21x^12 - 117x^10 - 54x^8 + 81x^6 + 54x^4 - 27	\( 2^{18}\cdot 3^{27}\cdot 1297^{2} \)	18T768	Trivial (GRH)
18.0.10145719923049728269615104.1	x^18 + 12x^16 + 54x^14 + 117x^12 + 134x^10 + 99x^8 + 73x^6 + 44x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.4.10145719923049728269615104.5	x^18 + 5x^16 - x^14 - 35x^12 - 71x^10 - 72x^8 - 30x^6 + 6x^4 + 7x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.8.10145719923049728269615104.9	x^18 + 5x^16 + 5x^14 - 37x^12 - 27x^10 + 85x^8 + 17x^6 - 54x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.0.10161075065555921079107584.1	x^18 + 15x^16 + 98x^14 + 360x^12 + 799x^10 + 1074x^8 + 834x^6 + 334x^4 + 53x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{2} \)	18T768	$[3]$ (GRH)
18.8.69140512696962724890148864.1	x^18 - 18x^14 + 3x^12 + 87x^10 - 22x^8 - 66x^6 + 3x^4 + 10x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 138041^{2} \)	18T768	Trivial (GRH)
18.14.71020039461348097887305728.1	x^18 - 12x^16 + 70x^14 - 261x^12 + 637x^10 - 972x^8 + 874x^6 - 427x^4 + 98x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.14.71020039461348097887305728.2	x^18 - 3x^16 - 33x^14 + 120x^12 + 193x^10 - 1167x^8 + 1499x^6 - 728x^4 + 126x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.10.71020039461348097887305728.5	x^18 - 6x^16 + 6x^14 + 23x^12 - 40x^10 - 17x^8 + 27x^6 + 49x^4 - 35x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.6.71020039461348097887305728.5	x^18 - 4x^16 - 28x^14 + 37x^12 + 301x^10 + 458x^8 + 258x^6 + 21x^4 - 28x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.10.71020039461348097887305728.6	x^18 - 9x^16 + 16x^14 + 46x^12 - 152x^10 + 33x^8 + 232x^6 - 210x^4 + 63x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.6.71020039461348097887305728.6	x^18 - 6x^16 + x^14 + 29x^12 - 20x^10 - 27x^8 + 50x^6 - 14x^4 - 56x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 52879^{2} \)	18T768	Trivial (GRH)
18.8.72096958561753534235452443.1	x^18 - 3x^17 + 9x^16 - 16x^15 - 3x^14 + 3x^13 - 23x^12 + 114x^11 + 153x^10 - 44x^9 - 558x^8 - 741x^7 + 556x^6 + 1917x^5 - 435x^4 - 1017x^3 + 12x^2 + 21x + 1	\( -\,3^{27}\cdot 73^{4}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.0.104192253035948620552339456.1	x^18 + 17x^16 + 114x^14 + 389x^12 + 728x^10 + 758x^8 + 433x^6 + 131x^4 + 19x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T768	$[16]$ (GRH)
18.4.104192253035948620552339456.2	x^18 + 15x^16 + 84x^14 + 213x^12 + 218x^10 - 11x^8 - 153x^6 - 72x^4 - 3x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T768	Trivial (GRH)
18.4.104192253035948620552339456.3	x^18 + 7x^16 + x^14 - 85x^12 - 226x^10 - 220x^8 - 66x^6 + 17x^4 + 11x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T768	Trivial (GRH)
18.10.3546591312668853157931778048.1	x^18 - 6x^16 - 36x^14 + 177x^12 - 18x^10 - 405x^8 + 45x^6 + 216x^4 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.14.3546591312668853157931778048.1	x^18 - 12x^16 + 417x^12 - 1377x^10 + 756x^8 + 2007x^6 - 2349x^4 + 567x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.6.3546591312668853157931778048.1	x^18 - 3x^16 - 27x^14 - 6x^12 + 153x^10 + 216x^8 - 54x^6 - 270x^4 - 162x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.10.3546591312668853157931778048.2	x^18 - 9x^16 + 9x^14 + 117x^12 - 306x^10 - 108x^8 + 639x^6 + 108x^4 - 243x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.14.3546591312668853157931778048.2	x^18 - 12x^16 + 36x^14 + 75x^12 - 594x^10 + 1134x^8 - 855x^6 + 162x^4 + 81x^2 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.6.3546591312668853157931778048.2	x^18 + 3x^16 - 18x^14 - 75x^12 + 9x^10 + 378x^8 + 585x^6 + 297x^4 - 27	\( 2^{18}\cdot 3^{27}\cdot 73^{2}\cdot 577^{2} \)	18T768	Trivial (GRH)
18.0.8933928336352529387966169088.1	x^18 + 19x^16 + 147x^14 + 604x^12 + 1442x^10 + 2050x^8 + 1700x^6 + 763x^4 + 154x^2 + 7	\( -\,2^{18}\cdot 7^{13}\cdot 593081^{2} \)	18T768	$[40]$ (GRH)
18.18.8933928336352529387966169088.1	x^18 - 19x^16 + 147x^14 - 604x^12 + 1442x^10 - 2050x^8 + 1700x^6 - 763x^4 + 154x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 593081^{2} \)	18T768	Trivial (GRH)
18.18.35737942791330376849452433408.1	x^18 - 35x^16 + 441x^14 - 2723x^12 + 9212x^10 - 17885x^8 + 19894x^6 - 12005x^4 + 3430x^2 - 343	\( 2^{18}\cdot 7^{15}\cdot 169457^{2} \)	18T768	Trivial (GRH)