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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
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)
21.3.4900609474961156001559784767.1	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)
21.9.155640552803090077912213347113.1	x^21 - x^20 + 3x^19 - 8x^17 + 11x^16 - 38x^15 - 57x^14 - 99x^13 - 54x^12 + 84x^11 + 86x^10 + 362x^9 - 80x^8 - 244x^7 + 140x^6 - 71x^5 + 3x^4 + 9x^3 - 7x^2 + 2x + 1	\( 7^{14}\cdot 71^{3}\cdot 8623^{3} \)	21T56	Trivial (GRH)
21.9.155896945048377999491545839641.1	x^21 - 15x^19 - 4x^18 + 93x^17 + 12x^16 - 281x^15 + 63x^14 + 375x^13 - 266x^12 - 23x^11 + 432x^10 - 39x^9 - 220x^8 - 298x^7 + 36x^6 + 171x^5 + 26x^4 - 33x^3 - 1	\( 7^{14}\cdot 593^{3}\cdot 1033^{3} \)	21T56	Trivial (GRH)
21.15.8323171787619560684096554117351.1	x^21 - 15x^19 - 4x^18 + 67x^17 + 60x^16 - 81x^15 - 268x^14 + 17x^13 + 474x^12 - 514x^11 - 401x^10 + 1233x^9 + 103x^8 - 842x^7 - 75x^6 + 200x^5 + 73x^4 - 7x^3 - 19x^2 - 2x + 1	\( -\,7^{14}\cdot 107^{3}\cdot 21557^{3} \)	21T56	Trivial (GRH)
21.15.9019481696572641947795544614807.1	x^21 - 20x^19 + 135x^17 - 16x^16 - 350x^15 + 149x^14 + 182x^13 - 477x^12 + 307x^11 + 641x^10 + 150x^9 - 233x^8 - 566x^7 - 26x^6 + 272x^5 + 5x^4 - 31x^3 + 7x^2 - 2x - 1	\( -\,7^{14}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3} \)	21T56	Trivial (GRH)
21.21.5535899331867573439772694059695993.1	x^21 - x^20 - 32x^19 + 27x^18 + 371x^17 - 273x^16 - 2035x^15 + 1336x^14 + 5767x^13 - 3508x^12 - 8825x^11 + 4990x^10 + 7522x^9 - 3911x^8 - 3561x^7 + 1665x^6 + 894x^5 - 359x^4 - 106x^3 + 34x^2 + 4x - 1	\( 7^{14}\cdot 71^{3}\cdot 283583^{3} \)	21T56	Trivial (GRH)
21.21.10807233650734185519504921698416857.1	x^21 - 2x^20 - 33x^19 + 54x^18 + 423x^17 - 578x^16 - 2679x^15 + 3163x^14 + 8911x^13 - 9346x^12 - 15389x^11 + 14554x^10 + 13283x^9 - 11462x^8 - 5756x^7 + 4570x^6 + 1193x^5 - 870x^4 - 105x^3 + 64x^2 + 4x - 1	\( 3^{3}\cdot 7^{14}\cdot 8388019^{3} \)	21T56	Trivial (GRH)