Number field search results

Results (1-50 of 669 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
7.1.844691575.1	x^7 - x^6 + 6x^5 - 7x^4 + x^3 - 9x^2 - 7x + 28	$7$	[1,3]	$-\,5^{2}\cdot 7\cdot 13^{6}$	$3$	$18.8470158004$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$245.612133191$
7.1.1655595487.1	x^7 - 3x^6 + 2x^5 + 6x^4 + 3x^3 - 16x^2 - 7x - 7	$7$	[1,3]	$-\,7^{3}\cdot 13^{6}$	$2$	$20.7488228124$			not computed	$D_{7}$ (as 7T2)	trivial	$2$	$3$	$149.983509716$
7.1.2471326208.1	x^7 - 2x^6 - 2x^5 - 4x^4 + 3x^3 - 2x^2 - 6x - 4	$7$	[1,3]	$-\,2^{9}\cdot 13^{6}$	$2$	$21.9708648976$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$885.346568835$
7.1.6424482779.1	x^7 - 3x^6 + 2x^5 - 7x^4 + 42x^3 - 3x^2 - 267x + 344	$7$	[1,3]	$-\,11^{3}\cdot 13^{6}$	$2$	$25.1837116719$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$483.950728717$
7.1.16290480375.1	x^7 - 2x^6 - 2x^5 + 22x^4 - 23x^3 + 76x^2 - 6x + 9	$7$	[1,3]	$-\,3^{3}\cdot 5^{3}\cdot 13^{6}$	$3$	$28.7638952639$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$1309.03075408$
7.1.16681451904.1	x^7 - x^6 - 7x^5 + 19x^4 + 27x^3 - 61x^2 - 33x + 67	$7$	[1,3]	$-\,2^{7}\cdot 3^{3}\cdot 13^{6}$	$3$	$28.8615147827$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$1071.33245716$
7.3.23477598976.1	x^7 - x^6 - 7x^5 - 7x^4 + 27x^3 + 69x^2 - 85x - 37	$7$	[3,2]	$2^{8}\cdot 13^{6}\cdot 19$	$3$	$30.3055349338$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$920.329109109$
7.1.24631206327.1	x^7 - 3x^6 + 15x^5 - 20x^4 - 36x^3 - 3x^2 + 84x + 45	$7$	[1,3]	$-\,3^{6}\cdot 7\cdot 13^{6}$	$3$	$30.5139165792$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$845.712097099$
7.1.33107082931.1	x^7 - 13x^5 - 13x^4 + 130x^3 + 221x^2 - 234x - 468	$7$	[1,3]	$-\,13^{6}\cdot 19^{3}$	$2$	$31.8306747723$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$1570.7428269$
7.1.38614472000.1	x^7 - x^6 + 6x^5 - 20x^4 + x^3 + 43x^2 - 20x - 50	$7$	[1,3]	$-\,2^{6}\cdot 5^{3}\cdot 13^{6}$	$3$	$32.5381510967$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$5807.69103062$
7.3.48871441125.1	x^7 - 13x^4 - 26x^3 - 39x^2 - 39x - 13	$7$	[3,2]	$3^{4}\cdot 5^{3}\cdot 13^{6}$	$3$	$33.6517673642$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$858.147471717$
7.3.50044355712.1	x^7 - x^6 + 6x^5 - 20x^4 + x^3 - 9x^2 + 6x + 2	$7$	[3,2]	$2^{7}\cdot 3^{4}\cdot 13^{6}$	$3$	$33.7659754472$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$2956.52690929$
7.1.66725807616.1	x^7 - x^6 + 19x^5 - 7x^4 + 118x^3 - 22x^2 + 240x - 24	$7$	[1,3]	$-\,2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$				$D_{7}$ (as 7T2)	trivial	$2$	$3$	$14660.1665751$
7.1.66725807616.2	x^7 - x^6 - 7x^5 + 19x^4 - 12x^3 + 4x^2 - 20x + 28	$7$	[1,3]	$-\,2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$				$S_7$ (as 7T7)	trivial	$2$	$3$	$3457.69876433$
7.1.66725807616.3	x^7 - x^6 + 6x^5 - 20x^4 + 27x^3 - 87x^2 + 97x - 167	$7$	[1,3]	$-\,2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$1239.86242434$
7.1.66725807616.4	x^7 - 3x^6 + 15x^5 - 7x^4 + 42x^3 + 36x^2 + 162x + 162	$7$	[1,3]	$-\,2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$				$S_7$ (as 7T7)	trivial	$2$	$3$	$5518.23374265$
7.3.66725807616.1	x^7 - 2x^6 - 2x^5 - 4x^4 - 36x^3 + 24x^2 + 72x + 48	$7$	[3,2]	$2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$				$S_7$ (as 7T7)	trivial	$2$	$4$	$4457.49187$
7.3.66725807616.2	x^7 - 2x^6 - 15x^5 + 22x^4 - 36x^3 + 24x^2 - 6x - 4	$7$	[3,2]	$2^{9}\cdot 3^{3}\cdot 13^{6}$	$3$	$35.1825806012$				$S_7$ (as 7T7)	trivial	$2$	$4$	$8766.61285636$
7.1.81124178863.1	x^7 - 3x^6 - 11x^5 + 32x^4 + 3x^3 - 94x^2 + 136x - 72	$7$	[1,3]	$-\,7^{5}\cdot 13^{6}$	$2$	$36.1784573708$			not computed	$F_7$ (as 7T4)	trivial	$2$	$3$	$1811.41517058$
7.1.105958111168.1	x^7 - 3x^6 + 2x^5 - 20x^4 + 81x^3 + 23x^2 - 384x + 448	$7$	[1,3]	$-\,2^{6}\cdot 7^{3}\cdot 13^{6}$	$3$	$37.5853996536$				$S_7$ (as 7T7)	trivial	$2$	$3$	$5727.3333545$
7.3.139012099200.1	x^7 - x^6 - 7x^5 - 7x^4 + 27x^3 + 69x^2 - 189x + 171	$7$	[3,2]	$2^{7}\cdot 3^{2}\cdot 5^{2}\cdot 13^{6}$	$4$	$39.0719113926$				$S_7$ (as 7T7)	trivial	$2$	$4$	$7099.99680901$
7.1.143795466919.1	x^7 - 2x^6 + 11x^5 - 43x^4 + 133x^3 - 236x^2 + 254x - 121	$7$	[1,3]	$-\,13^{6}\cdot 31^{3}$	$2$	$39.2612026997$			not computed	$D_{7}$ (as 7T2)	trivial	$2$	$3$	$1049.16405325$
7.3.158343469245.1	x^7 - x^6 + 6x^5 - 7x^4 + x^3 - 9x^2 - 33x + 15	$7$	[3,2]	$3^{8}\cdot 5\cdot 13^{6}$	$3$	$39.8054812952$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$4518.21316798$
7.3.173461035033.1	x^7 - 2x^6 - 2x^5 + 35x^4 - 114x^3 + 180x^2 - 84x + 9	$7$	[3,2]	$3^{3}\cdot 11^{3}\cdot 13^{6}$	$3$	$40.3274049458$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$2166.32948793$
7.1.178553318528.1	x^7 - x^6 - 7x^5 + 19x^4 + 27x^3 - 35x^2 + 19x + 41	$7$	[1,3]	$-\,2^{7}\cdot 13^{6}\cdot 17^{2}$	$3$	$40.4944419185$			not computed	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$1144.68521904$
7.1.200177422848.1	x^7 - 2x^6 + 11x^5 + 22x^4 - 23x^3 - 54x^2 - 45x + 126	$7$	[1,3]	$-\,2^{9}\cdot 3^{4}\cdot 13^{6}$	$3$	$41.1611851177$				$S_7$ (as 7T7)	trivial	$2$	$3$	$7935.86620092$
7.3.200177422848.1	x^7 - 3x^6 + 2x^5 + 6x^4 - 36x^3 + 36x^2 - 72x - 72	$7$	[3,2]	$2^{9}\cdot 3^{4}\cdot 13^{6}$	$3$	$41.1611851177$				$S_7$ (as 7T7)	trivial	$2$	$4$	$15483.5903556$
7.3.247132620800.1	x^7 - x^6 - 20x^5 - 20x^4 + 66x^3 + 30x^2 + 6x + 2	$7$	[3,2]	$2^{11}\cdot 5^{2}\cdot 13^{6}$	$3$	$42.4190989593$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$6604.31839676$
7.1.253349550792.1	x^7 - x^6 + 6x^5 - 7x^4 + 40x^3 - 87x^2 + 32x - 128	$7$	[1,3]	$-\,2^{3}\cdot 3^{8}\cdot 13^{6}$	$3$	$42.5699242067$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$3626.60646262$
7.1.253349550792.2	x^7 - x^6 + 6x^5 - 7x^4 + 40x^3 + 30x^2 + 32x - 128	$7$	[1,3]	$-\,2^{3}\cdot 3^{8}\cdot 13^{6}$	$3$	$42.5699242067$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$3388.17307479$
7.1.266903230464.1	x^7 - 2x^6 - 2x^5 - 4x^4 + 68x^3 + 24x^2 + 72x - 368	$7$	[1,3]	$-\,2^{11}\cdot 3^{3}\cdot 13^{6}$	$3$	$42.888046143$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$3073.35461793$
7.1.337799401056.1	x^7 - x^6 + 6x^5 - 20x^4 - 25x^3 - 9x^2 + 162x + 54	$7$	[1,3]	$-\,2^{5}\cdot 3^{7}\cdot 13^{6}$	$3$	$44.3558869469$			not computed	$S_7$ (as 7T7)	$[2]$	$2$	$3$	$7569.63284677$
7.1.370853389088.1	x^7 - x^6 + 6x^5 - 46x^4 - 12x^3 + 56x^2 - 72x - 128	$7$	[1,3]	$-\,2^{5}\cdot 7^{4}\cdot 13^{6}$	$3$	$44.9513955096$				$S_7$ (as 7T7)	trivial	$2$	$3$	$18789.6785794$
7.3.402309703341.1	x^7 - x^6 - 20x^5 - 7x^4 + 157x^3 + 290x^2 + 84x - 63	$7$	[3,2]	$3^{5}\cdot 7^{3}\cdot 13^{6}$	$3$	$45.4772670791$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$6066.300513$
7.1.450399201408.1	x^7 - 3x^6 + 15x^5 - 7x^4 + 42x^3 + 114x^2 + 136x - 72	$7$	[1,3]	$-\,2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$				$S_7$ (as 7T7)	trivial	$2$	$3$	$7894.54020179$
7.1.450399201408.2	x^7 - x^6 - 7x^5 + 19x^4 - 25x^3 + 17x^2 - 33x + 93	$7$	[1,3]	$-\,2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$				$S_7$ (as 7T7)	trivial	$2$	$3$	$14311.682056$
7.3.450399201408.1	x^7 - 2x^6 - 15x^5 - 4x^4 + 146x^3 + 24x^2 - 656x + 568	$7$	[3,2]	$2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$				$S_7$ (as 7T7)	trivial	$2$	$4$	$15661.8464578$
7.3.450399201408.2	x^7 - 2x^6 - 15x^5 + 48x^4 + 120x^3 - 288x^2 - 864x - 576	$7$	[3,2]	$2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$8342.96424145$
7.3.450399201408.3	x^7 - x^6 + 19x^5 - 7x^4 + 40x^3 - 22x^2 - 72x - 24	$7$	[3,2]	$2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$				$S_7$ (as 7T7)	trivial	$2$	$4$	$26304.622658$
7.3.450399201408.4	x^7 - 2x^6 + 24x^5 + 48x^4 - 75x^3 + 24x^2 + 150x + 48	$7$	[3,2]	$2^{7}\cdot 3^{6}\cdot 13^{6}$	$3$	$46.2167773025$				$S_7$ (as 7T7)	trivial	$2$	$4$	$19639.0597735$
7.3.463373664000.1	x^7 - x^6 + 6x^5 + 58x^4 - 90x^3 - 152x^2 - 46x + 2	$7$	[3,2]	$2^{8}\cdot 3\cdot 5^{3}\cdot 13^{6}$	$4$	$46.4046627753$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$15805.0927283$
7.3.484379936768.1	x^7 - 3x^6 - 11x^5 - 7x^4 - 49x^3 - 237x^2 + 409x + 1553	$7$	[3,2]	$2^{11}\cdot 7^{2}\cdot 13^{6}$	$3$	$46.6995081603$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$5059.84024511$
7.3.484379936768.2	x^7 - 2x^6 - 15x^5 - 4x^4 + 29x^3 - 2x^2 - 149x - 56	$7$	[3,2]	$2^{11}\cdot 7^{2}\cdot 13^{6}$	$3$	$46.6995081603$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$15726.1975447$
7.1.501133790807.1	x^7 - x^6 + 6x^5 + 6x^4 - 38x^3 + 108x^2 - 202x + 145	$7$	[1,3]	$-\,13^{6}\cdot 47^{3}$	$2$	$46.9269097026$			not computed	$D_{7}$ (as 7T2)	trivial	$2$	$3$	$1330.90810011$
7.1.600532268544.1	x^7 - 3x^6 + 2x^5 + 32x^4 - 23x^3 - 107x^2 - 735x + 1943	$7$	[1,3]	$-\,2^{9}\cdot 3^{5}\cdot 13^{6}$	$3$	$48.1557387588$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$5737.41606647$
7.3.600532268544.1	x^7 - 2x^6 - 2x^5 - 4x^4 - 10x^3 - 28x^2 + 72x + 48	$7$	[3,2]	$2^{9}\cdot 3^{5}\cdot 13^{6}$	$3$	$48.1557387588$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$5982.17199472$
7.1.617831552000.1	x^7 - x^6 + 6x^5 - 20x^4 + 40x^3 - 100x^2 + 110x - 50	$7$	[1,3]	$-\,2^{10}\cdot 5^{3}\cdot 13^{6}$	$3$	$48.3515067088$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$6194.98581835$
7.3.617831552000.1	x^7 - 78x^4 + 13x^3 + 260x^2 - 130x + 130	$7$	[3,2]	$2^{10}\cdot 5^{3}\cdot 13^{6}$	$3$	$48.3515067088$			not computed	$S_7$ (as 7T7)	trivial	$2$	$4$	$9693.20238196$
7.1.724021350000.1	x^7 - 3x^6 + 2x^5 - 20x^4 + 55x^3 - 29x^2 + 162x - 228	$7$	[1,3]	$-\,2^{4}\cdot 3\cdot 5^{5}\cdot 13^{6}$	$4$	$49.4595540367$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$10564.051166$
7.1.756843651200.1	x^7 - x^6 + 6x^5 - 20x^4 + 40x^3 - 48x^2 + 32x - 24	$7$	[1,3]	$-\,2^{7}\cdot 5^{2}\cdot 7^{2}\cdot 13^{6}$	$4$	$49.7738095528$			not computed	$S_7$ (as 7T7)	trivial	$2$	$3$	$10896.4058751$