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
18.0.303256405652583481344.1	x^18 + 6x^16 + 15x^14 + 17x^12 + 3x^10 - 12x^8 - 2x^6 + 15x^4 + 9x^2 + 1	\( -\,2^{30}\cdot 3^{24} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.0.1792881348741312102875.1	x^18 + 10x^16 - 4x^15 + 50x^14 - 8x^13 + 143x^12 + 6x^11 + 286x^10 + 38x^9 + 346x^8 - 2x^7 + 241x^6 - 18x^5 + 72x^4 - 11x^3 + 12x^2 + 1	\( -\,5^{3}\cdot 7^{13}\cdot 23^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.6.2426051245220667850752.1	x^18 + 3x^16 - 23x^12 + 30x^8 + 32x^6 - 84x^4 + 48x^2 - 8	\( 2^{33}\cdot 3^{24} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.6.4570752111750967984128.1	x^18 - 10x^16 + 35x^14 - 73x^12 + 135x^10 - 240x^8 + 324x^6 - 279x^4 + 135x^2 - 27	\( 2^{24}\cdot 3^{9}\cdot 7^{12} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.12.105226667788517176205647.1	x^18 - 8x^17 + 21x^16 - 15x^15 - 25x^14 + 82x^13 - 132x^12 + 80x^11 + 56x^10 - 131x^9 + 153x^8 - 99x^7 + 61x^6 - 93x^5 + 21x^4 + 62x^3 - 37x^2 + 3x + 1	\( -\,7^{15}\cdot 53^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.12.429456733437258587406367.1	x^18 - 3x^17 - 7x^16 + 34x^15 - 35x^14 - 42x^13 + 146x^12 + 32x^11 - 240x^10 - 164x^9 + 112x^8 + 146x^7 + 105x^6 + 174x^5 + 108x^4 - 27x^3 - 45x^2 - 13x - 1	\( -\,7^{15}\cdot 67^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
18.0.1256584347701942722269184.1	x^18 + 17x^16 + 117x^14 + 421x^12 + 854x^10 + 979x^8 + 601x^6 + 177x^4 + 23x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	$C_6\times S_4$ (as 18T61)	$[2]$
18.6.5852021141154776996728512.1	x^18 + 12x^16 + 33x^14 - 63x^12 - 351x^10 - 360x^8 + 39x^6 + 189x^4 + 54x^2 - 3	\( 2^{6}\cdot 3^{31}\cdot 23^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.6.15605389709746071991276032.1	x^18 + 6x^16 - 9x^14 - 84x^12 - 69x^10 + 153x^8 + 201x^6 + 24x^4 - 36x^2 - 8	\( 2^{9}\cdot 3^{30}\cdot 23^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial
18.18.279992823820843547402730217.1	x^18 - 4x^17 - 19x^16 + 93x^15 + 70x^14 - 668x^13 + 255x^12 + 1811x^11 - 1506x^10 - 2121x^9 + 2524x^8 + 876x^7 - 1788x^6 + 174x^5 + 468x^4 - 169x^3 - 4x^2 + 9x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
18.18.431008431261766353738330112.1	x^18 - 5x^17 - 17x^16 + 116x^15 + 28x^14 - 898x^13 + 729x^12 + 2639x^11 - 3688x^10 - 2725x^9 + 6303x^8 - 110x^7 - 4279x^6 + 1433x^5 + 961x^4 - 464x^3 - 59x^2 + 35x + 1	\( 2^{12}\cdot 7^{15}\cdot 53^{6} \)	$C_6\times S_4$ (as 18T61)	Trivial (GRH)
18.0.823903027170640554647911051.1	x^18 + 17x^16 - 7x^15 + 174x^14 - 142x^13 + 1276x^12 - 1068x^11 + 6618x^10 - 6859x^9 + 25026x^8 - 25559x^7 + 58530x^6 - 44688x^5 + 47915x^4 - 20759x^3 + 14724x^2 - 2412x + 216	\( -\,7^{12}\cdot 53^{6}\cdot 139^{3} \)	$C_6\times S_4$ (as 18T61)	$[2, 2, 10]$ (GRH)