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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.80282147152292264089.1	x^18 - x^17 + 4x^16 - x^15 + 6x^14 - 4x^13 + 10x^12 - 6x^11 + x^10 - 3x^9 + 2x^8 - 7x^7 - 10x^6 + x^5 - 9x^4 - 4x^2 - 2x - 1	\( 31^{6}\cdot 67^{6} \)	18T711	Trivial
18.2.3221287037577650765824.3	x^18 - x^16 + 2x^14 + 4x^12 - 9x^10 + 17x^8 - 19x^6 + 4x^4 + x^2 - 1	\( 2^{18}\cdot 31^{6}\cdot 61^{4} \)	18T711	Trivial (GRH)
18.6.3221287037577650765824.3	x^18 - 2x^16 - 5x^14 + 11x^12 - 2x^10 - 11x^8 + 21x^6 - 18x^4 + 7x^2 - 1	\( 2^{18}\cdot 31^{6}\cdot 61^{4} \)	18T711	Trivial (GRH)
18.6.3435531027183254634496.3	x^18 - 5x^16 + 11x^14 - 17x^12 + 18x^10 - 14x^8 + x^6 + 8x^4 - x^2 - 1	\( 2^{18}\cdot 23^{6}\cdot 97^{4} \)	18T711	Trivial (GRH)
18.10.17298154203755513310784.1	x^18 + 2x^16 - 16x^14 - 26x^12 + 73x^10 + 57x^8 - 132x^6 + 33x^4 + 8x^2 - 1	\( 2^{6}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.1107081869040352851890176.1	x^18 - 16x^16 + 95x^14 - 253x^12 + 273x^10 - 10x^8 - 169x^6 + 89x^4 - 8x^2 - 1	\( 2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.6.1107081869040352851890176.2	x^18 + 11x^16 + 36x^14 + 2x^12 - 181x^10 - 262x^8 - 58x^6 + 75x^4 + 28x^2 - 1	\( 2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.1107081869040352851890176.3	x^18 - 4x^16 - 4x^14 + 22x^12 - x^10 - 31x^8 + 4x^6 + 15x^4 - 1	\( 2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.6.1107081869040352851890176.3	x^18 + 2x^16 - 22x^14 - 82x^12 - 51x^10 + 116x^8 + 152x^6 + 35x^4 - 11x^2 - 1	\( 2^{12}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.70853239618582582520971264.1	x^18 + 4x^16 - 9x^14 - 28x^12 + 44x^10 + 33x^8 - 70x^6 + 26x^4 + x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.2.70853239618582582520971264.1	x^18 + 9x^16 + 21x^14 - 25x^12 - 182x^10 - 303x^8 - 229x^6 - 85x^4 - 15x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	$[2]$ (GRH)
18.6.70853239618582582520971264.1	x^18 + x^16 - 21x^14 - 45x^12 + 30x^10 + 105x^8 + 29x^6 - 33x^4 - 13x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.70853239618582582520971264.2	x^18 - 16x^14 + 15x^12 + 68x^10 - 120x^8 + 12x^6 + 70x^4 - 28x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.2.70853239618582582520971264.2	x^18 + 14x^16 + 67x^14 + 125x^12 + 12x^10 - 272x^8 - 366x^6 - 190x^4 - 37x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	$[2, 2]$ (GRH)
18.6.70853239618582582520971264.2	x^18 + 9x^16 + 21x^14 - 17x^12 - 134x^10 - 185x^8 - 77x^6 + 15x^4 + 9x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.70853239618582582520971264.3	x^18 - 5x^16 - x^14 + 36x^12 - 39x^10 - 44x^8 + 77x^6 - 12x^4 - 11x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.70853239618582582520971264.3	x^18 - 13x^16 + 47x^14 - 30x^12 - 95x^10 + 120x^8 + 25x^6 - 76x^4 + 23x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.70853239618582582520971264.4	x^18 - 7x^16 + 4x^14 + 43x^12 - 24x^10 - 95x^8 - 4x^6 + 33x^4 - 3x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.70853239618582582520971264.4	x^18 - 6x^16 + 5x^14 + 35x^12 - 88x^10 + 52x^8 + 36x^6 - 46x^4 + 13x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.14.70853239618582582520971264.5	x^18 - 11x^16 + 34x^14 + 16x^12 - 255x^10 + 452x^8 - 290x^6 + 35x^4 + 18x^2 - 1	\( 2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.6.1588991331185396666448931454976.1	x^18 + 11x^16 - 28x^14 - 450x^12 - 1029x^10 - 107x^8 + 1355x^6 + 726x^4 - 119x^2 - 49	\( 2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \)	18T711	$[2]$ (GRH)
18.18.1588991331185396666448931454976.2	x^18 - 32x^16 + 397x^14 - 2438x^12 + 8021x^10 - 14812x^8 + 15332x^6 - 8282x^4 + 1855x^2 - 49	\( 2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \)	18T711	Trivial (GRH)
18.6.1588991331185396666448931454976.2	x^18 + 9x^16 - 51x^14 - 158x^12 + 546x^10 + 906x^8 - 1505x^6 - 1743x^4 - 525x^2 - 49	\( 2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \)	18T711	$[2]$ (GRH)
18.18.1588991331185396666448931454976.3	x^18 - 25x^16 + 249x^14 - 1281x^12 + 3721x^10 - 6276x^8 + 6048x^6 - 3108x^4 + 721x^2 - 49	\( 2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \)	18T711	Trivial (GRH)