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 matches 1-50 of 5409)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.176339497789.1	x^12 - 3x^11 + 2x^10 + 4x^8 - 6x^7 + 5x^5 - 5x^4 + 4x^2 - 2x + 1	\( 7^{8}\cdot 13^{2}\cdot 181 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.205567038859.1	x^12 - x^11 + 2x^10 + x^8 + 4x^7 - 5x^6 + 4x^5 - 8x^4 + 4x^3 - 4x^2 + 2x - 1	\( -\,7^{8}\cdot 13^{2}\cdot 211 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.285455651117.1	x^12 - 4x^11 + 11x^10 - 22x^9 + 36x^8 - 47x^7 + 51x^6 - 47x^5 + 36x^4 - 22x^3 + 11x^2 - 4x + 1	\( 7^{8}\cdot 13^{2}\cdot 293 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.299095170283.1	x^12 - 2x^11 + 4x^10 - x^9 - 2x^8 + 6x^7 - 4x^6 - 2x^5 + 2x^4 - 2x^3 - 2x^2 + 1	\( -\,7^{8}\cdot 13^{2}\cdot 307 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.823612912893.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 9x^8 + 12x^7 - 11x^6 + 6x^5 + 3x^4 - 12x^3 + 12x^2 - 6x + 1	\( 3^{16}\cdot 19^{2}\cdot 53 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.884706715067.1	x^12 - x^11 + 2x^10 - 2x^9 + 4x^8 - 5x^7 + 7x^6 - 4x^5 + 2x^4 - 5x^3 + 4x^2 - 3x + 1	\( -\,7^{8}\cdot 43^{2}\cdot 83 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.968117620736.1	x^12 - 2x^11 - x^10 + 4x^9 + 4x^8 - 14x^7 + 5x^6 + 14x^5 - 15x^4 + 8x^2 - 2x - 1	\( 2^{12}\cdot 7^{8}\cdot 41 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.1158384877741.1	x^12 - 2x^11 - 2x^10 + 4x^9 + 2x^8 - 3x^7 + 3x^6 - 10x^4 + x^3 + 7x^2 + x - 1	\( 7^{8}\cdot 13^{2}\cdot 29\cdot 41 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.1337647129637.1	x^12 - 3x^11 + 2x^10 + 5x^9 - 17x^8 + 27x^7 - 28x^6 + 14x^5 + 3x^4 - 10x^3 + 4x^2 + 2x - 1	\( 7^{8}\cdot 13^{2}\cdot 1373 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.1481617269811.1	x^12 - x^11 + 4x^10 + x^9 + 2x^8 + 10x^7 + 9x^5 + 4x^4 + 6x^3 + 2x^2 + 2x + 1	\( -\,7^{8}\cdot 43^{2}\cdot 139 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.1929300185869.1	x^12 - x^11 + 2x^9 - 5x^8 - x^7 + 5x^6 - 4x^5 - 4x^4 + 5x^3 + 4x^2 - 1	\( 7^{8}\cdot 43^{2}\cdot 181 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.2455188392293.1	x^12 - 2x^11 - x^10 + 6x^9 - 6x^8 - x^7 + 5x^6 - x^5 - 6x^4 + 6x^3 - x^2 - 2x + 1	\( 7^{8}\cdot 13\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.3061353657357.1	x^12 - 3x^11 + 3x^10 + 3x^8 - 6x^6 + 3x^5 + 2x^3 - 3x - 1	\( 3^{16}\cdot 19^{2}\cdot 197 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.4018487127473.1	x^12 - x^11 + 3x^10 - x^9 + 4x^8 - 2x^7 + 5x^6 - 2x^5 + 4x^4 - x^3 + 3x^2 - x + 1	\( 7^{8}\cdot 13\cdot 29\cdot 43^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.4466170043531.1	x^12 - 2x^11 - 4x^10 + 10x^9 + 3x^8 - 22x^7 + 7x^6 + 22x^5 - 17x^4 - 8x^3 + 11x^2 - x - 1	\( -\,7^{8}\cdot 43^{2}\cdot 419 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.4770738948267.1	x^12 - 3x^10 - 4x^9 + 12x^7 + x^6 - 3x^5 + 3x^4 - 7x^3 - 3x^2 + 3x + 1	\( -\,3^{16}\cdot 19^{2}\cdot 307 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.5259925493221.1	x^12 - x^11 - x^10 + x^8 + 2x^7 + 3x^6 - 11x^5 + 11x^4 - 7x^3 + 5x^2 - 3x + 1	\( 7^{8}\cdot 71^{2}\cdot 181 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.5476958721269.1	x^12 - 2x^10 - 5x^8 - 7x^7 - 3x^6 - 7x^5 - 5x^4 - 2x^2 + 1	\( 7^{8}\cdot 29\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.8121007759123.1	x^12 - 2x^11 - 2x^10 + 4x^9 - 2x^8 + 7x^7 - 14x^5 + 6x^4 + 3x^3 - 4x^2 + x + 1	\( -\,7^{8}\cdot 43\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.13409105834831.1	x^12 - 4x^11 + 5x^10 - 10x^8 + 18x^7 - 11x^6 - 16x^5 + 22x^4 - 8x^2 + x + 1	\( -\,7^{8}\cdot 71\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.13409105834831.1	x^12 - 3x^11 + 4x^10 - 6x^9 + 8x^8 - 9x^7 + 9x^6 - 9x^5 + 8x^4 - 6x^3 + 4x^2 - 3x + 1	\( -\,7^{8}\cdot 71\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.15675433581563.1	x^12 - 4x^11 + 7x^10 - 9x^9 + 9x^8 - 8x^7 + 7x^6 - 8x^5 + 9x^4 - 9x^3 + 7x^2 - 4x + 1	\( -\,7^{8}\cdot 83\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.18319482619417.1	x^12 - x^11 - 8x^10 + 6x^9 + 26x^8 - 15x^7 - 39x^6 + 19x^5 + 20x^4 - 6x^3 - 3x + 1	\( 7^{8}\cdot 97\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.20290998443009.1	x^12 - 2x^11 - 7x^10 + 10x^9 + 21x^8 - 18x^7 - 24x^6 + 16x^5 + 7x^4 - 10x^3 + 4x + 1	\( 7^{8}\cdot 41\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.20802722533376.1	x^12 - 2x^11 - 6x^10 + 14x^9 + 10x^8 - 46x^7 - 18x^6 + 58x^5 + 22x^4 - 28x^3 - 9x^2 + 4x + 1	\( 2^{12}\cdot 7^{8}\cdot 881 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.25438761101997.1	x^12 - 3x^10 - x^9 - 9x^8 + 12x^7 + 21x^6 - 12x^5 - 9x^4 + x^3 - 3x^2 + 1	\( 3^{16}\cdot 19^{2}\cdot 1637 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.29100190851109.1	x^12 + x^10 - 5x^9 - 2x^8 - 8x^7 + 5x^6 + 8x^5 + 23x^4 + 6x^3 - 7x + 7	\( 7^{8}\cdot 167^{2}\cdot 181 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.31539727808687.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 4x^8 - 21x^6 + 22x^5 + 3x^4 - 12x^3 + 12x^2 - 4x - 1	\( -\,7^{8}\cdot 167\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.6.45137694289079.1	x^12 - x^11 - 5x^10 + 3x^9 + 15x^8 + 4x^7 - 23x^6 - 19x^5 + 13x^4 + 20x^3 - 3x^2 - 7x + 1	\( -\,7^{8}\cdot 181^{2}\cdot 239 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.47106938781077.1	x^12 - x^11 + 3x^10 + 8x^9 - 2x^8 + 8x^7 + 9x^6 - 8x^5 - 2x^4 - 8x^3 + 3x^2 + x + 1	\( 7^{8}\cdot 167^{2}\cdot 293 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.55336169149373.1	x^12 - 3x^11 + 4x^9 + 2x^7 - 10x^6 + 3x^5 + 21x^4 - 4x^3 - 14x^2 - 2x + 1	\( 7^{8}\cdot 181^{2}\cdot 293 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.55336169149373.1	x^12 - 2x^11 + 3x^9 - 7x^8 + 17x^7 - 17x^6 + 2x^5 + 4x^3 - 3x + 1	\( 7^{8}\cdot 181^{2}\cdot 293 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.89577334589869.1	x^12 - x^11 - 4x^10 + 13x^9 - 24x^8 + 33x^7 - 37x^6 + 33x^5 - 24x^4 + 13x^3 - 4x^2 - x + 1	\( 7^{8}\cdot 181\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.8.89577334589869.1	x^12 - 3x^11 - 4x^10 + 12x^9 + 14x^8 - 18x^7 - 39x^6 + 15x^5 + 49x^4 - 5x^3 - 22x^2 - 2x + 1	\( 7^{8}\cdot 181\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.10.104424406621339.1	x^12 - 6x^11 + 10x^10 + 3x^9 - 29x^8 + 35x^7 + 7x^6 - 49x^5 + 19x^4 + 18x^3 - 9x^2 - 2x + 1	\( -\,7^{8}\cdot 211\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.10.119171067348991.1	x^12 - 11x^10 - 4x^9 + 37x^8 + 20x^7 - 54x^6 - 27x^5 + 35x^4 + 13x^3 - 10x^2 - 2x + 1	\( -\,7^{8}\cdot 181^{2}\cdot 631 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.293300582556233.1	x^12 - 3x^11 + 5x^10 - 4x^9 + 4x^8 - 9x^7 + 19x^6 - 18x^5 + 16x^4 - 32x^3 + 80x^2 - 96x + 64	\( 7^{8}\cdot 181^{2}\cdot 1553 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.436009015324169.1	x^12 - 3x^11 + 6x^10 - 13x^9 + 23x^8 - 38x^7 + 61x^6 - 76x^5 + 92x^4 - 104x^3 + 96x^2 - 96x + 64	\( 7^{8}\cdot 293^{2}\cdot 881 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.4.436680211169792.1	x^12 - 5x^10 + 4x^8 + 19x^6 - 23x^4 - 20x^2 + 8	\( 2^{9}\cdot 31^{8} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.451943524827473.1	x^12 - x^11 + 2x^10 + x^9 + 2x^8 + x^7 + 9x^6 + 2x^5 + 8x^4 + 8x^3 + 32x^2 - 32x + 64	\( 7^{8}\cdot 181^{2}\cdot 2393 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.507846275913529.1	x^12 - 5x^11 + 14x^10 - 26x^9 + 36x^8 - 40x^7 + 49x^6 - 80x^5 + 144x^4 - 208x^3 + 224x^2 - 160x + 64	\( 7^{8}\cdot 181^{2}\cdot 2689 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.12.637026957477253.1	x^12 - x^11 - 12x^10 + 8x^9 + 51x^8 - 20x^7 - 89x^6 + 23x^5 + 64x^4 - 13x^3 - 17x^2 + 3x + 1	\( 7^{8}\cdot 181^{2}\cdot 3373 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.637929194952161.1	x^12 + 3x^10 + x^8 - 7x^7 - 3x^6 - 14x^5 + 4x^4 + 48x^2 + 64	\( 7^{8}\cdot 293^{2}\cdot 1289 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.870382701745569.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 3x^8 - 12x^7 + 33x^6 - 24x^5 - 12x^4 + 16x^3 + 48x^2 - 96x + 64	\( 3^{16}\cdot 197^{2}\cdot 521 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.2.873360422339584.1	x^12 - 2x^10 - 5x^8 + 7x^6 + 14x^4 - 7x^2 - 16	\( -\,2^{10}\cdot 31^{8} \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.12.1272443408263937.1	x^12 - 2x^11 - 11x^10 + 18x^9 + 37x^8 - 52x^7 - 51x^6 + 58x^5 + 32x^4 - 24x^3 - 9x^2 + 3x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 1553 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.0.1702956441023537.1	x^12 + 4x^10 + 8x^8 - 7x^7 + 17x^6 - 14x^5 + 32x^4 + 64x^2 + 64	\( 7^{8}\cdot 71\cdot 127\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	$[2]$
12.0.2070101535994121.1	x^12 - 2x^11 + 5x^10 - 4x^9 + 11x^8 - 13x^7 + 33x^6 - 26x^5 + 44x^4 - 32x^3 + 80x^2 - 64x + 64	\( 7^{8}\cdot 97\cdot 113\cdot 181^{2} \)	$D_4\wr C_3$ (as 12T222)	$[2]$
12.0.2149962333087296.1	x^12 - x^11 + 2x^10 + x^9 + 2x^8 - 6x^7 + 16x^6 - 12x^5 + 8x^4 + 8x^3 + 32x^2 - 32x + 64	\( 2^{6}\cdot 7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 41 \)	$D_4\wr C_3$ (as 12T222)	$[2]$
12.0.2292882824060017.1	x^12 - 5x^11 + 15x^10 - 34x^9 + 67x^8 - 116x^7 + 177x^6 - 232x^5 + 268x^4 - 272x^3 + 240x^2 - 160x + 64	\( 7^{8}\cdot 41\cdot 113\cdot 293^{2} \)	$D_4\wr C_3$ (as 12T222)	$[2]$