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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.70840057834604343296.1	x^18 - x^17 + 2x^16 - 5x^15 + 4x^14 - 6x^13 + 20x^12 - 3x^11 + 19x^10 - 45x^9 - 16x^8 - 13x^7 + 34x^6 + 25x^5 - 3x^4 - 13x^3 - x^2 + x + 1	\( -\,2^{12}\cdot 11^{7}\cdot 31^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.0.415117688652320997376.1	x^18 - 2x^17 + 2x^16 + 4x^15 - 9x^14 + 8x^13 + 22x^12 + 6x^11 + x^10 + 18x^9 + 46x^8 + 46x^7 + 39x^6 + 34x^5 + 32x^4 + 32x^3 + 24x^2 + 10x + 2	\( -\,2^{18}\cdot 11^{6}\cdot 19^{7} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.4.9393890619437282308096.1	x^18 - 2x^17 + 2x^16 + 2x^15 - 14x^13 + 45x^12 - 18x^11 - 46x^10 + 84x^9 - 18x^8 - 38x^7 + 59x^6 + 16x^5 - 28x^4 - 2x^3 + 10x^2 - 1	\( -\,2^{12}\cdot 19^{7}\cdot 37^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.4.26131210597134370603008.1	x^18 + 6x^16 + 12x^14 - 12x^13 - 15x^12 - 24x^11 - 18x^10 + 32x^9 + 12x^8 + 30x^7 + 3x^6 - 18x^5 + 6x^2 + 6x + 1	\( -\,2^{18}\cdot 3^{25}\cdot 7^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.0.35782043924083219755008.1	x^18 - 3x^17 - 4x^15 + 25x^14 - 9x^13 - 2x^12 - 53x^11 + 44x^10 - 15x^9 + 36x^8 - 101x^7 + 118x^6 + 85x^5 + 163x^4 + 34x^2 + 11x + 5	\( -\,2^{12}\cdot 23^{7}\cdot 37^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.6.345097791077487520043008.1	x^18 - 3x^16 + 9x^14 - 44x^12 + 52x^10 - 191x^8 + 263x^6 + 317x^4 + 10x^2 - 37	\( 2^{12}\cdot 31^{6}\cdot 37^{7} \)	$S_3\times S_4$ (as 18T65)	Trivial (GRH)
18.6.29531293631851085903947077.1	x^18 - 9x^16 - 31x^15 - 27x^14 + 108x^13 + 324x^12 + 66x^11 - 696x^10 - 942x^9 - 72x^8 + 1185x^7 + 329x^6 - 687x^5 + 120x^4 - 36x^3 + 39x^2 - 3	\( 3^{19}\cdot 31^{11} \)	$S_3\times S_4$ (as 18T65)	Trivial (GRH)
18.6.412762523693292700085997568.1	x^18 - 12x^15 - 16x^14 + 72x^13 - 141x^12 - 112x^11 + 800x^10 - 44x^9 - 1080x^8 + 496x^7 + 579x^6 - 408x^5 + 64x^4 + 52x^3 - 16x^2 + 1	\( 2^{12}\cdot 37^{7}\cdot 101^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.6.412762523693292700085997568.2	x^18 + 16x^16 + 48x^14 - 95x^12 - 516x^10 - 184x^8 + 1179x^6 + 1232x^4 + 212x^2 - 37	\( 2^{12}\cdot 37^{7}\cdot 101^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial
18.0.1511989339484099453953241088.1	x^18 + 6x^16 - 12x^14 + 28x^12 + 345x^10 + 138x^8 + 14812x^6 + 39675x^4 + 36501x^2 + 12167	\( -\,2^{12}\cdot 3^{18}\cdot 23^{11} \)	$S_3\times S_4$ (as 18T65)	$[14]$ (GRH)
18.18.26416801516370732805503844352.1	x^18 - 31x^16 + 375x^14 - 2329x^12 + 8172x^10 - 16724x^8 + 19864x^6 - 13168x^4 + 4448x^2 - 592	\( 2^{18}\cdot 37^{7}\cdot 101^{6} \)	$S_3\times S_4$ (as 18T65)	Trivial (GRH)
18.18.6920314220367728205834398990336.1	x^18 - 32x^16 + 392x^14 - 2363x^12 + 7600x^10 - 13268x^8 + 12275x^6 - 5776x^4 + 1276x^2 - 101	\( 2^{18}\cdot 17^{6}\cdot 101^{9} \)	$S_3\times S_4$ (as 18T65)	$[2]$ (GRH)