Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.46110822453.1	x^12 - 2x^11 + x^10 + x^9 + x^8 - 5x^7 + 6x^6 - 4x^5 + 4x^4 - 5x^3 + 5x^2 - 3x + 1	\( 3^{6}\cdot 63252157 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.0.46580196393.1	x^12 - 3x^10 - x^9 + 5x^8 + x^7 - 7x^6 - x^5 + 8x^4 + 2x^3 - 4x^2 - x + 1	\( 3^{6}\cdot 157\cdot 406981 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.0.110375328125.1	x^12 - 3x^11 + 5x^10 - 4x^9 + x^8 + 3x^7 - 2x^6 - 4x^5 + 10x^4 - 12x^3 + 9x^2 - 4x + 1	\( 5^{6}\cdot 2531\cdot 2791 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.0.167661390625.1	x^12 - x^10 - x^9 + 2x^8 + 4x^7 - 2x^6 - 2x^5 - x^4 + x^2 - x + 1	\( 5^{6}\cdot 10730329 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.2.225117671875.1	x^12 - x^10 - x^9 - x^8 + 3x^7 + 3x^6 - 2x^4 - 2x^3 - 1	\( -\,5^{6}\cdot 179\cdot 80489 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.2.239557046875.1	x^12 - x^10 - x^9 + 2x^7 - 2x^6 + x^4 + x^3 - x + 1	\( -\,5^{6}\cdot 19\cdot 806929 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.794230140625.1	x^12 - x^9 - 4x^8 + x^7 + 2x^6 + 2x^5 + x^4 - x^3 - 2x^2 - x + 1	\( 5^{6}\cdot 50830729 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.854660453125.1	x^12 - 2x^11 + 6x^9 - 6x^8 - 6x^7 + 14x^6 - 5x^5 - 9x^4 + 10x^3 - x^2 - 4x + 1	\( 5^{6}\cdot 54698269 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.1095605453125.1	x^12 - 2x^11 - x^10 + 8x^9 - 9x^8 + x^7 + 9x^6 - 9x^5 + 4x^4 + x^3 - 2x^2 + x - 1	\( 5^{6}\cdot 70118749 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.4.1538611578125.1	x^12 - x^11 - 3x^10 + 4x^9 + x^8 - 7x^7 + 7x^5 - x^4 - 6x^3 + 3x + 1	\( 5^{6}\cdot 61\cdot 1614281 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.4008072671875.1	x^12 - 4x^10 - 4x^9 + x^8 + 8x^7 + 8x^6 + x^5 - 5x^4 - 6x^3 - 2x^2 + 1	\( -\,5^{6}\cdot 61\cdot 4205191 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.4457810171875.1	x^12 - 3x^11 + 2x^10 + 3x^9 - 8x^8 + 3x^7 + 7x^6 + x^5 - 4x^4 - 5x^3 + x + 1	\( -\,5^{6}\cdot 31\cdot 101\cdot 91121 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.9120427796875.1	x^12 - x^11 - x^10 - x^9 + 2x^8 - 2x^7 - 3x^6 + 19x^5 - 21x^4 + 6x^3 + 6x^2 - 5x + 1	\( -\,5^{6}\cdot 19\cdot 79\cdot 388879 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.8.24805630328125.1	x^12 - 3x^11 + x^9 + 5x^8 + 8x^7 - 8x^6 - 8x^5 - 5x^4 - 2x^3 + 6x^2 + 5x + 1	\( 5^{6}\cdot 2731\cdot 581311 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.6.24913847046875.1	x^12 - 3x^11 - 2x^10 + 13x^9 - 10x^8 - 11x^7 + 29x^6 - 9x^5 - 22x^4 + 16x^3 + 3x^2 - 5x + 1	\( -\,5^{6}\cdot 9859\cdot 161729 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.8.26641409828125.1	x^12 - x^11 - 2x^10 + 6x^9 - 4x^8 - 2x^7 - 4x^6 - 10x^5 + 20x^4 + 7x^3 - 11x^2 + 1	\( 5^{6}\cdot 1705050229 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.8.30967526064128.1	x^12 - 6x^10 - 2x^9 + 9x^8 + 8x^7 - x^6 - 14x^5 - 6x^4 + 10x^3 + 5x^2 - 2x - 1	\( 2^{18}\cdot 118131737 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.8.56034909078125.1	x^12 - x^11 - 2x^10 - 2x^9 + 6x^8 + 5x^7 - 16x^6 + 8x^5 + 17x^4 - 14x^3 - 8x^2 + 4x + 1	\( 5^{6}\cdot 9649\cdot 371669 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.10.115472708921875.1	x^12 - 10x^10 - 2x^9 + 33x^8 + 12x^7 - 43x^6 - 23x^5 + 19x^4 + 17x^3 - 4x - 1	\( -\,5^{6}\cdot 7390253371 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.10.173022521421875.1	x^12 - 2x^11 - 6x^10 + 13x^9 + 10x^8 - 30x^7 + 2x^6 + 30x^5 - 16x^4 - 13x^3 + 9x^2 + 2x - 1	\( -\,5^{6}\cdot 6679\cdot 1657949 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.12.696248958578125.1	x^12 - 12x^10 + 51x^8 - 2x^7 - 94x^6 + 12x^5 + 74x^4 - 20x^3 - 19x^2 + 9x - 1	\( 5^{6}\cdot 241\cdot 3329\cdot 55541 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.12.803483858453125.1	x^12 - 13x^10 + 55x^8 - 2x^7 - 99x^6 + 8x^5 + 76x^4 - 9x^3 - 20x^2 + 3x + 1	\( 5^{6}\cdot 601\cdot 85562341 \)	$S_6\wr C_2$ (as 12T299)	Trivial