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 matches 1-50 of 3072)

Label	Polynomial	Discriminant	Galois group	Class group
12.8.16135716339712.1	x^12 - 2x^11 - 3x^10 + 10x^9 - 11x^8 + 2x^7 + 24x^6 - 38x^5 + 31x^4 - 20x^3 - 2x^2 + 8x - 1	\( 2^{18}\cdot 367^{2}\cdot 457 \)	12T260	Trivial
12.8.17497403356237.1	x^12 - x^11 - 9x^10 + 9x^9 + 30x^8 - 29x^7 - 46x^6 + 39x^5 + 33x^4 - 19x^3 - 10x^2 + 2x + 1	\( 7^{2}\cdot 373\cdot 30941^{2} \)	12T293	Trivial
12.8.18137291911168.1	x^12 - 4x^10 - 2x^9 + 9x^8 + 2x^7 - 15x^6 + 8x^5 + 14x^4 - 10x^3 - 7x^2 + 2x + 1	\( 2^{12}\cdot 151\cdot 2237\cdot 13109 \)	$S_{12}$ (as 12T301)	Trivial
12.8.18172175140625.1	x^12 - x^11 - 4x^10 + 5x^9 - 2x^8 + 15x^6 - 15x^5 - 10x^4 + 14x^3 - x^2 - 4x + 1	\( 5^{6}\cdot 11^{2}\cdot 109^{2}\cdot 809 \)	12T260	Trivial
12.8.18277154559581.1	x^12 - 2x^11 - 3x^10 + 6x^9 - 3x^7 + 3x^6 - x^5 + 4x^4 - 4x^3 - 3x^2 + 4x - 1	\( 18277154559581 \)	$S_{12}$ (as 12T301)	Trivial
12.8.18308160781573.1	x^12 - x^11 - 7x^10 + 7x^9 + 10x^8 - 14x^7 + 2x^6 + 19x^5 - 8x^4 - 17x^3 + x^2 + 5x + 1	\( 13^{2}\cdot 397\cdot 16519^{2} \)	12T293	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
12.8.19063047515625.1	x^12 - 2x^11 - 5x^10 + 7x^9 + 10x^8 + 2x^7 - 20x^6 - 19x^5 + 20x^4 + 19x^3 - 5x^2 - 6x - 1	\( 3^{4}\cdot 5^{6}\cdot 3881^{2} \)	12T203	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
12.8.21426070716181.1	x^12 - 2x^11 - 2x^10 + 2x^9 - x^8 + 18x^7 + 3x^6 - 44x^5 + x^4 + 32x^3 - 3x^2 - 5x + 1	\( 61\cdot 592661^{2} \)	12T293	Trivial
12.8.24302560546048.1	x^12 - x^11 - 4x^10 + 10x^9 - 5x^8 - 26x^7 + 29x^6 + 10x^5 - 23x^4 + 12x^3 + 2x^2 - 5x + 1	\( 2^{8}\cdot 37^{7} \)	$A_4:C_4$ (as 12T30)	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
12.8.24952387024669.1	x^12 - 6x^11 + 14x^10 - 15x^9 + 24x^7 - 30x^6 + 9x^5 + 13x^4 - 16x^3 + 3x^2 + 3x - 1	\( 13^{10}\cdot 181 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	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
12.8.25641035447233.1	x^12 - 5x^11 + 6x^10 + 6x^9 - 18x^8 + 17x^7 - 15x^6 + 17x^5 - 18x^4 + 6x^3 + 6x^2 - 5x + 1	\( 73\cdot 592661^{2} \)	12T293	Trivial
12.8.25652742953125.1	x^12 - 5x^11 + 3x^10 + 22x^9 - 41x^8 + 6x^7 + 39x^6 - 35x^5 + 3x^4 + 18x^3 - 5x^2 - 6x - 1	\( 5^{6}\cdot 109\cdot 3881^{2} \)	12T260	Trivial
12.8.25652742953125.2	x^12 - 4x^11 + 16x^9 - 9x^8 - 30x^7 + 22x^6 + 31x^5 - 23x^4 - 13x^3 + 10x^2 + x - 1	\( 5^{6}\cdot 109\cdot 3881^{2} \)	12T260	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
12.8.28866785588221.1	x^12 - 6x^10 - 4x^9 + 13x^8 + 16x^7 - 9x^6 - 21x^5 - 4x^4 + 11x^3 + 5x^2 - 2x - 1	\( 7^{8}\cdot 5007421 \)	12T292	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
12.8.31436180453125.1	x^12 - 2x^11 - 2x^10 + 2x^9 - 7x^8 + 6x^7 + 23x^6 - x^5 - 24x^4 - 9x^3 + 9x^2 + 4x - 1	\( 5^{6}\cdot 7^{8}\cdot 349 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.8.34183776846541.1	x^12 - 4x^11 + 3x^10 + 2x^9 - 7x^8 + 11x^7 - 11x^6 - x^5 + 21x^4 - 9x^3 - 8x^2 + 2x + 1	\( 7^{8}\cdot 181^{3} \)	$C_4\times C_4^2:C_3$ (as 12T94)	Trivial
12.8.34282488765625.1	x^12 - x^11 - 5x^10 + 7x^9 + x^8 - 11x^7 + 19x^6 - 14x^5 - 5x^4 + 30x^3 - 27x^2 + 5x + 1	\( 5^{6}\cdot 31^{2}\cdot 1511^{2} \)	12T203	Trivial
12.8.34801233152049.1	x^12 - 3x^11 - 4x^10 + 16x^9 + 4x^8 - 24x^7 - x^6 - 4x^5 - 10x^4 + 26x^3 + 31x^2 + 10x + 1	\( 3^{6}\cdot 7^{10}\cdot 13^{2} \)	$C_2^2 \times A_4$ (as 12T25)	Trivial
12.8.35258133876736.1	x^12 - 3x^10 + x^8 - 6x^6 + 11x^4 - 6x^2 + 1	\( 2^{12}\cdot 92779^{2} \)	12T285	Trivial
12.8.36472323149824.1	x^12 - 6x^10 + 13x^8 - 15x^6 + 14x^4 - 9x^2 + 1	\( 2^{12}\cdot 197^{2}\cdot 479^{2} \)	12T285	Trivial
12.8.36767438995456.1	x^12 - 4x^11 - 2x^10 + 20x^9 + x^8 - 46x^7 - 2x^6 + 58x^5 + 3x^4 - 34x^3 + x^2 + 6x - 1	\( 2^{18}\cdot 13^{2}\cdot 911^{2} \)	12T236	Trivial
12.8.37921581578125.1	x^12 - x^11 - 5x^10 + 9x^9 + 9x^8 - 20x^7 - 11x^6 + 9x^5 + 9x^4 + 7x^3 - x^2 - 4x - 1	\( 5^{6}\cdot 7^{8}\cdot 421 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.8.38509781640625.1	x^12 - x^11 - 7x^10 + 4x^9 + 8x^8 - 13x^7 + 9x^6 + 21x^5 - 18x^4 - 12x^3 + 8x^2 + 2x - 1	\( 5^{8}\cdot 9929^{2} \)	12T203	Trivial
12.8.39358370640625.1	x^12 - 2x^11 - 8x^10 + 20x^9 + 8x^8 - 38x^7 + 2x^6 + 20x^5 + 3x^4 + x^3 - 6x^2 - x + 1	\( 5^{6}\cdot 31^{2}\cdot 1619^{2} \)	12T203	Trivial
12.8.40147924665121.1	x^12 - 5x^11 + 6x^10 + 9x^9 - 33x^8 + 36x^7 + 6x^6 - 51x^5 + 22x^4 + 19x^3 - 2x^2 - 8x + 1	\( 7^{10}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.8.40419192196881.1	x^12 - 6x^11 + 12x^10 - 45x^8 + 81x^7 - 25x^6 - 69x^5 + 48x^4 + 21x^3 - 18x^2 + 1	\( 3^{18}\cdot 17^{2}\cdot 19^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.8.41524582203125.1	x^12 - 3x^11 - 5x^10 + 20x^9 + 3x^8 - 40x^7 + 11x^6 + 15x^5 + 3x^4 + 13x^3 - 26x^2 + 10x - 1	\( 5^{6}\cdot 7^{8}\cdot 461 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.8.42597674078125.1	x^12 - x^11 - 5x^10 + 5x^9 + 3x^8 + x^7 + 6x^6 - 17x^5 - 8x^4 + 15x^3 + 5x^2 - 3x - 1	\( 5^{6}\cdot 181\cdot 3881^{2} \)	12T260	Trivial
12.8.44804009850925.1	x^12 - 4x^11 + 3x^10 + x^9 - 4x^8 + 3x^7 + x^6 + 9x^5 + 3x^4 - 12x^3 - 4x^2 + 3x + 1	\( 5^{2}\cdot 13^{11} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.8.44962053890625.1	x^12 - 5x^11 + 4x^10 + 14x^9 - 22x^8 - 7x^7 + 29x^6 - 7x^5 - 22x^4 + 14x^3 + 4x^2 - 5x + 1	\( 3^{2}\cdot 5^{6}\cdot 17881^{2} \)	12T236	Trivial
12.8.45358541265625.1	x^12 - 5x^11 + 3x^10 + 14x^9 - 11x^8 - 19x^7 + 3x^6 + 26x^5 + 9x^4 - 21x^3 - 7x^2 + 5x + 1	\( 5^{6}\cdot 7^{2}\cdot 43^{2}\cdot 179^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.8.47211387828125.1	x^12 - 6x^10 - 3x^9 + 11x^8 + 16x^7 - 6x^6 - 24x^5 - 4x^4 + 11x^3 + 5x^2 - x - 1	\( 5^{6}\cdot 29^{3}\cdot 229\cdot 541 \)	12T274	Trivial
12.8.47466656328125.1	x^12 - x^11 - 7x^10 + 8x^9 + 17x^8 - 15x^7 - 32x^6 - 4x^5 + 49x^4 + 26x^3 - 30x^2 - 12x - 1	\( 5^{7}\cdot 157^{4} \)	$C_4\times S_4$ (as 12T53)	Trivial
12.8.51942673828125.1	x^12 - 2x^11 - 6x^10 + 11x^9 + 15x^8 - 17x^7 - 27x^6 + 4x^5 + 29x^4 + 4x^3 - 12x^2 + 1	\( 3^{6}\cdot 5^{9}\cdot 191^{2} \)	$S_3^2:C_4$ (as 12T79)	Trivial
12.8.52649684000000.1	x^12 - 8x^10 - 3x^9 + 21x^8 + 14x^7 - 21x^6 - 18x^5 + 5x^4 + 3x^3 + x^2 + 3x + 1	\( 2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 101 \)	12T208	Trivial
12.8.53626953329261.1	x^12 - x^11 - 2x^10 + 8x^9 - 10x^8 - 19x^7 + 26x^6 + 23x^5 - 22x^4 - 12x^3 + 8x^2 + 2x - 1	\( 13^{10}\cdot 389 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.8.53894294828125.1	x^12 - 5x^11 + 5x^10 + 9x^9 - 17x^8 + x^7 + 12x^6 - 4x^5 - 2x^4 - 5x^3 + x^2 + 4x + 1	\( 5^{6}\cdot 229\cdot 3881^{2} \)	12T260	Trivial
12.8.54738442953125.1	x^12 - 6x^11 + 12x^10 - 5x^9 - 21x^8 + 48x^7 - 48x^6 + 21x^5 + 10x^4 - 22x^3 + 6x^2 + 4x - 1	\( 5^{6}\cdot 29^{3}\cdot 379^{2} \)	$D_6\wr C_2$ (as 12T125)	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
12.8.56034909078125.1	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
12.8.56819956000000.1	x^12 - x^11 - 5x^10 + x^9 + 9x^8 + 12x^7 - 5x^6 - 32x^5 - 3x^4 + 27x^3 + 2x^2 - 6x + 1	\( 2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 109 \)	12T208	Trivial
12.8.58003456000000.1	x^12 - 4x^11 + 2x^10 + 4x^9 + 12x^8 - 26x^7 - 22x^6 + 72x^5 - 32x^4 - 32x^3 + 27x^2 - 2x - 1	\( 2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 17^{2} \)	$C_2\times S_3\wr C_2$ (as 12T77)	Trivial
12.8.59967600015625.1	x^12 - 4x^11 + 4x^10 - 3x^9 + x^8 + 21x^7 - 13x^6 - 21x^5 + x^4 + 3x^3 + 4x^2 + 4x + 1	\( 5^{6}\cdot 41^{2}\cdot 1511^{2} \)	12T236	Trivial