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 785)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.198015149549.1	x^12 - 5x^11 + 13x^10 - 19x^9 + 16x^8 - 6x^7 + 6x^6 - 23x^5 + 43x^4 - 44x^3 + 26x^2 - 8x + 1	\( 7^{10}\cdot 701 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.209594484549.1	x^12 - 3x^10 - 4x^9 + 9x^8 + 18x^7 + 6x^6 - 18x^5 - 9x^4 + 5x^3 + 9x^2 - 6x + 1	\( 3^{18}\cdot 541 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.2612175453125.1	x^12 - 3x^11 + 9x^9 - 12x^8 + x^7 + 7x^6 + x^5 - 12x^4 + 9x^3 - 3x + 1	\( 5^{6}\cdot 7^{8}\cdot 29 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.3693075640625.1	x^12 - x^11 - x^10 - 3x^9 - 6x^8 - 6x^7 - 9x^6 - 6x^5 - 6x^4 - 3x^3 - x^2 - x + 1	\( 5^{6}\cdot 7^{8}\cdot 41 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.6395326109375.1	x^12 - 4x^11 + 17x^9 - 14x^8 - 23x^7 + 32x^6 + 4x^5 - 21x^4 + 11x^3 - 5x + 1	\( -\,5^{6}\cdot 7^{8}\cdot 71 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.7306500067997.1	x^12 - 4x^11 + 5x^10 + 3x^9 - 14x^8 + 7x^7 + 15x^6 - 20x^5 + 12x^4 - 3x^3 - 8x^2 + 4x + 1	\( 13^{10}\cdot 53 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.10890820856071.1	x^12 - 4x^11 + 2x^10 + 13x^9 - 27x^8 + 15x^7 + 22x^6 - 42x^5 + 27x^4 - 11x^2 + 6x - 1	\( -\,13^{10}\cdot 79 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.12520427171875.1	x^12 - x^11 - 3x^10 + x^9 + 2x^8 + 10x^7 - 7x^6 - 12x^5 + 11x^4 - x^3 - 5x^2 + 2x + 1	\( -\,5^{6}\cdot 7^{8}\cdot 139 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.16303577828125.1	x^12 - 5x^11 + 11x^10 - 15x^9 + 14x^8 - 5x^7 + 3x^6 - 30x^5 + 49x^4 - 20x^3 - 10x^2 + 5x + 1	\( 5^{6}\cdot 7^{8}\cdot 181 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.21527928734375.1	x^12 - 5x^11 + 7x^10 + 7x^9 - 35x^8 + 44x^7 - 9x^6 - 49x^5 + 87x^4 - 70x^3 + 13x^2 + 11x - 1	\( -\,5^{6}\cdot 7^{8}\cdot 239 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.21643783220293.1	x^12 - 2x^11 - x^10 + 9x^9 - 21x^8 + 32x^7 - 37x^6 + 32x^5 - 21x^4 + 9x^3 - x^2 - 2x + 1	\( 13^{10}\cdot 157 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.22608828921875.1	x^12 - 4x^11 + 7x^10 - 6x^9 + x^8 + 3x^7 - 18x^6 + 31x^5 - 8x^4 - 15x^3 + 16x^2 - 8x + 1	\( -\,5^{6}\cdot 7^{8}\cdot 251 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	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
12.8.31436180453125.1	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
12.2.37741431546875.1	x^12 - 6x^11 + 24x^10 - 65x^9 + 129x^8 - 192x^7 + 206x^6 - 153x^5 + 69x^4 - 10x^3 - 8x^2 + 5x - 1	\( -\,5^{6}\cdot 7^{8}\cdot 419 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	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
12.8.41524582203125.1	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
12.8.53626953329261.1	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
12.2.59359435296875.1	x^12 - x^11 + x^10 - 5x^9 + 17x^8 - 9x^7 - 2x^6 - 9x^5 - 9x^4 - 13x^3 - 7x^2 - 4x - 1	\( -\,5^{6}\cdot 7^{8}\cdot 659 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.8.63142585953125.1	x^12 - 4x^11 + 3x^10 - 2x^9 + 9x^8 + 13x^7 - 31x^6 - 6x^5 + 3x^4 + 18x^3 + x^2 - 5x - 1	\( 5^{6}\cdot 7^{8}\cdot 701 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.133848398109375.1	x^12 - 6x^11 + 12x^10 - x^9 - 36x^8 + 63x^7 - 44x^6 - 3x^5 + 36x^4 - 21x^3 - 6x^2 + 3x + 1	\( -\,3^{16}\cdot 5^{6}\cdot 199 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.168600935531327.1	x^12 - 4x^11 - x^10 + 23x^9 - 26x^8 - 23x^7 + 56x^6 - 6x^5 - 39x^4 + 11x^3 + 10x^2 - 2x - 1	\( -\,13^{10}\cdot 1223 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.172770619021119.1	x^12 - x^11 - 10x^10 + 7x^9 + 33x^8 - 12x^7 - 50x^6 + x^5 + 38x^4 + 7x^3 - 12x^2 - 2x + 1	\( -\,3^{6}\cdot 7^{10}\cdot 839 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.227079114390625.1	x^12 - 4x^11 + 10x^10 - 14x^9 + 10x^8 + 9x^7 - 25x^6 + 18x^5 + 40x^4 - 112x^3 + 160x^2 - 128x + 64	\( 5^{6}\cdot 7^{8}\cdot 2521 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.4.294052163113917.1	x^12 - 5x^11 + 14x^10 - 25x^9 + 34x^8 - 42x^7 + 24x^6 - 11x^5 + 5x^4 + 18x^3 + 14x^2 - x - 1	\( 3^{3}\cdot 13^{10}\cdot 79 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.382008141265625.1	x^12 - 3x^11 + 6x^10 - 6x^9 + 9x^8 - 17x^7 + 33x^6 - 34x^5 + 36x^4 - 48x^3 + 96x^2 - 96x + 64	\( 5^{6}\cdot 7^{8}\cdot 4241 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.430256353060729.1	x^12 - 5x^11 + 17x^10 - 44x^9 + 93x^8 - 166x^7 + 253x^6 - 332x^5 + 372x^4 - 352x^3 + 272x^2 - 160x + 64	\( 13^{10}\cdot 3121 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.2.564668382613504.1	x^12 + 4x^10 - 2x^8 - 22x^6 - 24x^4 - 9x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.564668382613504.1	x^12 - 4x^10 - 2x^8 + 22x^6 - 24x^4 + 9x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.564668382613504.2	x^12 - x^10 - 5x^8 + 4x^6 + 6x^4 - 3x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.564668382613504.3	x^12 + x^10 - 5x^8 - 4x^6 + 6x^4 + 3x^2 - 1	\( -\,2^{12}\cdot 13^{10} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.12.870852093010133.1	x^12 - x^11 - 13x^10 + 15x^9 + 55x^8 - 70x^7 - 85x^6 + 115x^5 + 40x^4 - 50x^3 - 13x^2 + 4x + 1	\( 13^{10}\cdot 6317 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.12.1037754255015625.1	x^12 - 2x^11 - 12x^10 + 19x^9 + 49x^8 - 57x^7 - 82x^6 + 72x^5 + 53x^4 - 40x^3 - 9x^2 + 8x - 1	\( 5^{6}\cdot 7^{8}\cdot 41\cdot 281 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.1416001889763328.1	x^12 - 4x^11 + 8x^10 - 10x^9 + 13x^8 - 4x^7 + 19x^6 + 58x^5 + 122x^4 + 174x^3 + 185x^2 + 126x + 41	\( 2^{18}\cdot 7^{8}\cdot 937 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.6189907940737024.1	x^12 + 2x^10 - 13x^8 - 10x^6 + 52x^4 - 24x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.6189907940737024.1	x^12 - 8x^10 + 16x^8 + 10x^6 - 51x^4 + 34x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.2.6189907940737024.3	x^12 + 8x^10 + 16x^8 - 10x^6 - 51x^4 - 34x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.6189907940737024.8	x^12 - 2x^10 - 13x^8 + 10x^6 + 52x^4 + 24x^2 - 1	\( -\,2^{30}\cdot 7^{8} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.0.6523601692786529.1	x^12 - x^11 + 7x^10 - 6x^9 + 26x^8 - 19x^7 + 63x^6 - 38x^5 + 104x^4 - 48x^3 + 112x^2 - 32x + 64	\( 13^{10}\cdot 79\cdot 599 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	$[4]$
12.0.6721580185301961.1	x^12 - x^11 + 6x^10 - 4x^9 + 20x^8 - 12x^7 + 49x^6 - 24x^5 + 80x^4 - 32x^3 + 96x^2 - 32x + 64	\( 3^{6}\cdot 7^{11}\cdot 4663 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	$[4]$
12.10.7340688973975552.1	x^12 - 13x^10 + 52x^8 - 78x^6 + 26x^4 + 26x^2 - 13	\( -\,2^{12}\cdot 13^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.7340688973975552.1	x^12 - 13x^8 + 39x^4 - 13x^2 - 13	\( -\,2^{12}\cdot 13^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.2.7340688973975552.1	x^12 + 13x^10 + 52x^8 + 78x^6 + 26x^4 - 26x^2 - 13	\( -\,2^{12}\cdot 13^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.7340688973975552.4	x^12 - 13x^8 + 39x^4 + 13x^2 - 13	\( -\,2^{12}\cdot 13^{11} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.19499511680335872.1	x^12 - 6x^10 + 3x^8 + 24x^6 - 9x^4 - 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.19499511680335872.1	x^12 - 6x^10 + 3x^8 + 24x^6 - 36x^4 + 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.19499511680335872.2	x^12 + 6x^10 - 6x^8 - 42x^6 + 63x^4 - 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.10.19499511680335872.2	x^12 - 6x^10 + 3x^8 + 42x^6 - 90x^4 + 54x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.19499511680335872.5	x^12 + 6x^10 + 3x^8 - 24x^6 - 9x^4 + 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.6.19499511680335872.6	x^12 - 6x^10 - 6x^8 + 42x^6 + 63x^4 + 18x^2 - 3	\( -\,2^{24}\cdot 3^{19} \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial