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 47 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.8.9324056974004327.1	x^14 - x^13 - 4x^12 + 8x^11 + 2x^10 - 33x^9 + 7x^8 + 70x^7 - 2x^6 - 72x^5 - 9x^4 + 32x^3 + 6x^2 - 5x - 1	\( -\,23\cdot 71^{2}\cdot 283583^{2} \)	14T57	Trivial
14.8.11012732926484375.1	x^14 - 2x^13 - 2x^12 + 10x^11 - 8x^10 - 12x^9 + 23x^8 - 7x^7 - 16x^6 + 18x^5 - 8x^3 + 4x^2 + x - 1	\( -\,5^{7}\cdot 41\cdot 229\cdot 349\cdot 43019 \)	14T61	Trivial
14.8.16266899635859375.1	x^14 - 5x^13 + 7x^12 - 4x^11 + 15x^10 - 22x^9 - 11x^8 + 23x^7 - 9x^6 + 16x^5 - 6x^3 - 2x^2 - 3x - 1	\( -\,5^{7}\cdot 5011\cdot 41551849 \)	14T61	Trivial
14.8.17381743359198867.1	x^14 - 2x^13 - 5x^12 + 4x^11 + 18x^10 + 4x^9 - 30x^8 - 24x^7 + 22x^6 + 30x^5 - 16x^4 - 10x^3 + 11x^2 - x - 1	\( -\,3^{3}\cdot 11^{2}\cdot 107^{2}\cdot 21557^{2} \)	14T57	Trivial
14.8.28782958484969879.1	x^14 - 4x^13 + 4x^12 + 8x^11 - 30x^10 + 43x^9 - 35x^8 - 7x^7 + 56x^6 - 54x^5 - 4x^4 + 32x^3 - 8x^2 - 4x + 1	\( -\,71^{3}\cdot 283583^{2} \)	14T57	Trivial
14.8.87169416344387584.1	x^14 - 2x^12 - 3x^10 + 6x^8 - 9x^6 + 14x^4 - 7x^2 + 1	\( -\,2^{14}\cdot 107^{2}\cdot 21557^{2} \)	14T57	Trivial
14.8.258316958750207623.1	x^14 - 5x^13 + 6x^12 + 4x^11 - 19x^10 + 42x^9 - 40x^8 - 31x^7 + 79x^6 + 36x^5 - 175x^4 + 117x^3 - 19x^2 - 4x + 1	\( -\,7\cdot 577^{6} \)	14T38	Trivial
14.8.417195690175859375.1	x^14 - 3x^13 - 5x^12 + 18x^11 + 14x^10 - 52x^9 - 27x^8 + 91x^7 + 31x^6 - 86x^5 - 11x^4 + 40x^3 - 3x^2 - 8x + 1	\( -\,5^{7}\cdot 11\cdot 2939\cdot 5351\cdot 30869 \)	14T61	Trivial
14.8.1586804175179846827.1	x^14 - 7x^13 + 24x^12 - 53x^11 + 53x^10 + 54x^9 - 293x^8 + 551x^7 - 576x^6 + 309x^5 - x^4 - 118x^3 + 58x^2 - 2x - 1	\( -\,43\cdot 577^{6} \)	14T38	Trivial
14.8.1734413865894251183.1	x^14 - 4x^13 - 2x^12 + 17x^11 + 12x^10 - 48x^9 - 31x^8 + 80x^7 + 30x^6 - 65x^5 - 11x^4 + 26x^3 + 2x^2 - 5x - 1	\( -\,47\cdot 577^{6} \)	14T38	Trivial
14.8.1823606433479609375.1	x^14 - 5x^13 + 5x^12 + 11x^11 - 26x^10 + 17x^9 - 4x^8 - x^7 + 50x^6 - 95x^5 + x^4 + 76x^3 + 3x^2 - 18x - 4	\( -\,5^{7}\cdot 28579^{3} \)	$D_7 \wr C_2$ (as 14T20)	Trivial
14.8.4762110524569698304.1	x^14 - 4x^13 - 2x^12 + 8x^11 + x^10 + 18x^9 - 25x^8 + 4x^7 - 25x^6 + 18x^5 + x^4 + 8x^3 - 2x^2 - 4x + 1	\( -\,2^{14}\cdot 4129^{4} \)	14T51	Trivial
14.8.4762110524569698304.2	x^14 - x^12 - 31x^10 + 55x^8 + 23x^6 - 43x^4 - 13x^2 + 1	\( -\,2^{14}\cdot 4129^{4} \)	14T51	Trivial
14.8.6457923968755190575.1	x^14 - 6x^13 + 8x^12 + 19x^11 - 70x^10 + 78x^9 + 3x^8 - 110x^7 + 64x^6 + 123x^5 - 81x^4 - 136x^3 + 88x^2 + 45x - 25	\( -\,5^{2}\cdot 7\cdot 577^{6} \)	14T38	Trivial
14.8.8533901005667958784.1	x^14 - 3x^13 - 5x^12 + 18x^11 - 7x^10 + x^9 + 3x^8 + 71x^6 - 193x^5 - 59x^4 + 34x^3 + 35x^2 + 11x + 1	\( -\,2^{20}\cdot 19\cdot 809^{4} \)	14T51	Trivial
14.8.12272026890292239799.1	x^14 - 7x^13 + 17x^12 + 5x^11 - 129x^10 + 279x^9 - 59x^8 - 741x^7 + 1251x^6 - 237x^5 - 1340x^4 + 1237x^3 + 252x^2 - 733x - 109	\( -\,107^{3}\cdot 21557^{3} \)	14T54	Trivial
14.8.17919711399714597719.1	x^14 - 5x^13 + 46x^11 - 104x^10 - 9x^9 + 425x^8 - 655x^7 - 81x^6 + 1100x^5 - 778x^4 - 378x^3 + 416x^2 + 130x + 43	\( -\,61^{3}\cdot 42899^{3} \)	14T54	Trivial
14.8.18562159314367056979.1	x^14 - 3x^13 - 5x^12 + 36x^11 - 38x^10 - 102x^9 + 268x^8 - 69x^7 - 438x^6 + 421x^5 + 114x^4 - 244x^3 + 46x^2 + 29x - 8	\( -\,19\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.8.19048442098278793216.1	x^14 + 4x^12 - 50x^10 + 72x^8 + 73x^6 - 104x^4 - 16x^2 + 4	\( -\,2^{16}\cdot 4129^{4} \)	14T43	Trivial
14.8.19048442098278793216.2	x^14 + 4x^12 - 18x^10 - 20x^8 + 105x^6 - 76x^4 - 16x^2 + 16	\( -\,2^{16}\cdot 4129^{4} \)	14T43	Trivial
14.8.19273578224371707904.1	x^14 - 4x^13 - 7x^12 + 30x^11 + 6x^10 + 6x^9 - 35x^8 - 70x^7 - 35x^6 + 6x^5 + 6x^4 + 30x^3 - 7x^2 - 4x + 1	\( -\,2^{12}\cdot 19\cdot 3967^{4} \)	14T51	Trivial
14.8.22469982327918016343.1	x^14 - 3x^12 - 21x^10 + 75x^8 + 12x^6 - 173x^4 + 21x^2 + 92	\( -\,23\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.8.37474751954588984303.1	x^14 - 4x^13 - 7x^12 + 41x^11 + 11x^10 - 166x^9 + 25x^8 + 337x^7 - 98x^6 - 358x^5 + 113x^4 + 186x^3 - 54x^2 - 37x + 11	\( -\,218599\cdot 171431488499897 \)	14T63	Trivial
14.8.42938908405985984591.1	x^14 - 5x^13 - 2x^12 + 41x^11 - 23x^10 - 132x^9 + 106x^8 + 211x^7 - 172x^6 - 172x^5 + 121x^4 + 65x^3 - 34x^2 - 9x + 1	\( -\,23\cdot 49081\cdot 4208629\cdot 9037933 \)	14T63	Trivial
14.8.62761950191564959744.1	x^14 + x^12 - 20x^11 + 5x^10 + 22x^9 + 67x^8 - 30x^7 - 163x^6 + 38x^5 + 129x^4 - 2x^3 - 39x^2 - 12x - 1	\( -\,2^{12}\cdot 19\cdot 73^{8} \)	14T44	Trivial
14.8.62761950191564959744.2	x^14 - 7x^13 + 26x^12 - 65x^11 + 99x^10 - 66x^9 - 53x^8 + 179x^7 - 173x^6 + 30x^5 + 79x^4 - 73x^3 + 6x^2 + 17x + 1	\( -\,2^{12}\cdot 19\cdot 73^{8} \)	14T44	Trivial
14.8.70524602340782734375.1	x^14 - 14x^12 + 77x^10 - 210x^8 - 3x^7 + 294x^6 + 21x^5 - 196x^4 - 42x^3 + 49x^2 + 21x + 1	\( -\,5^{7}\cdot 7^{14}\cdot 11^{3} \)	14T32	Trivial
14.8.145343463601518854144.1	x^14 - 2x^13 - 15x^12 + 38x^11 + 55x^10 - 240x^9 + 75x^8 + 488x^7 - 613x^6 + 38x^5 + 407x^4 - 262x^3 - 11x^2 + 68x - 19	\( -\,2^{14}\cdot 11\cdot 73^{8} \)	14T44	Trivial
14.8.217031383311680000000.1	x^14 - 14x^12 + 77x^10 - 210x^8 - 2x^7 + 294x^6 + 14x^5 - 196x^4 - 28x^3 + 49x^2 + 14x - 4	\( -\,2^{12}\cdot 5^{7}\cdot 7^{14} \)	14T32	Trivial (GRH)
14.8.303899969348630331392.1	x^14 - 6x^13 - 3x^12 + 102x^11 - 281x^10 + 192x^9 + 343x^8 - 428x^7 - 625x^6 + 1330x^5 - 613x^4 + 6x^3 - 71x^2 + 36x + 1	\( -\,2^{14}\cdot 23\cdot 73^{8} \)	14T44	Trivial
14.8.618188512070319997156.1	x^14 - 6x^12 - 25x^10 + 196x^8 - 313x^6 + 17x^4 + 173x^2 + 4	\( -\,2^{2}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.8.773792930870360792667.1	x^14 - 3x^13 - 18x^12 + 28x^11 + 114x^10 - 104x^9 - 289x^8 + 119x^7 + 365x^6 + 104x^5 - 343x^4 - 175x^3 + 158x^2 + 61x - 17	\( -\,3^{7}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial
14.8.845634697317927878656.1	x^14 - 6x^13 + 12x^12 - 26x^11 + 110x^10 - 234x^9 + 248x^8 - 342x^7 + 538x^6 - 356x^5 + 186x^4 - 256x^3 + 64x^2 + 48x - 10	\( -\,2^{20}\cdot 73^{8} \)	$C_2\times F_8:C_3$ (as 14T18)	Trivial
14.8.845634697317927878656.2	x^14 - x^12 - 27x^10 + 51x^8 + 67x^6 - 115x^4 - 41x^2 + 1	\( -\,2^{20}\cdot 73^{8} \)	$C_2\times F_8:C_3$ (as 14T18)	Trivial
14.8.1081829896123059995023.1	x^14 - 19x^12 + 87x^10 - 68x^8 - 213x^6 + 142x^4 + 153x^2 + 28	\( -\,7^{9}\cdot 173^{6} \)	14T48	Trivial
14.8.1236377024140639994312.1	x^14 - 11x^12 - 5x^11 + 16x^10 + 106x^9 + 98x^8 - 326x^7 - 1116x^6 + 1552x^5 + 1784x^4 - 3304x^3 + 885x^2 + 579x - 127	\( -\,2^{3}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.8.2936395432334019986491.1	x^14 - 9x^12 - 12x^11 + 10x^10 + 203x^9 - 52x^8 - 740x^7 + 268x^6 + 840x^5 - 361x^4 - 279x^3 + 136x^2 + 21x - 10	\( -\,7^{8}\cdot 19\cdot 173^{6} \)	14T48	Trivial
14.8.5796901408038404767744.1	x^14 + x^12 - 12x^10 - 7x^8 + 28x^6 + 14x^4 - 9x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial (GRH)
14.8.5796901408038404767744.2	x^14 - 6x^12 + 3x^10 + 33x^8 - 49x^6 + 2x^4 + 16x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial (GRH)
14.8.5796901408038404767744.3	x^14 - 13x^12 + 31x^10 + 9x^8 - 54x^6 + 3x^4 + 23x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	Trivial
14.8.52251215374235323809792.1	x^14 - 4x^13 + 7x^12 - 14x^11 - 38x^10 + 132x^9 - 109x^8 + 230x^7 + 394x^6 - 580x^5 - 769x^4 + 474x^3 + 325x^2 - 52x - 8	\( -\,2^{14}\cdot 3^{7}\cdot 11^{3}\cdot 13^{6}\cdot 61^{3} \)	$D_7 \wr C_2$ (as 14T20)	Trivial
14.8.98547323936652881051648.1	x^14 - 3x^12 - 21x^10 + 73x^8 + 6x^6 - 125x^4 - 7x^2 + 17	\( -\,2^{14}\cdot 17\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial
14.8.98547323936652881051648.2	x^14 - 11x^12 + 27x^10 + 66x^8 - 286x^6 + 65x^4 + 354x^2 + 17	\( -\,2^{14}\cdot 17\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial
14.8.372085270290075144421376.1	x^14 - 22x^12 - 22x^11 + 192x^10 + 368x^9 - 942x^8 - 2056x^7 + 2479x^6 + 5908x^5 - 2018x^4 - 8254x^3 - 530x^2 + 3732x - 398	\( -\,2^{30}\cdot 809^{5} \)	14T42	Trivial
14.8.372085270290075144421376.2	x^14 + 8x^12 - 156x^10 - 300x^8 + 4660x^6 + 2128x^4 - 28928x^2 + 12944	\( -\,2^{30}\cdot 809^{5} \)	14T42	Trivial
14.8.194600400675149389603579413527667469123584.1	x^14 - 525x^12 - 518x^11 + 109942x^10 + 211890x^9 - 11363289x^8 - 32202766x^7 + 562633386x^6 + 2124722810x^5 - 8943505081x^4 - 47478809070x^3 - 109890439183x^2 - 304854167870x - 299096421324	\( -\,2^{16}\cdot 3^{8}\cdot 7^{10}\cdot 13^{7}\cdot 294467^{3} \)	14T45	Trivial (GRH)
14.8.1136553186048642579467300999397100786548736.1	x^14 - 2x^13 - 29x^12 + 2684x^11 - 50815x^10 - 101186x^9 + 2905773x^8 - 96986796x^7 + 393809153x^6 + 2822730482x^5 - 59621810879x^4 + 536849629536x^3 + 366359666251x^2 - 19410042679742x + 49980715777967	\( -\,2^{27}\cdot 7^{12}\cdot 409^{5}\cdot 3767^{3} \)	14T45	Trivial (GRH)