Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Results (1-50 of 2579 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
14.0.9095120158391.1	x^14 - 7x^13 + 25x^12 - 59x^11 + 103x^10 - 141x^9 + 159x^8 - 153x^7 + 129x^6 - 95x^5 + 58x^4 - 27x^3 + 10x^2 - 3x + 1	$14$	[0,7]	$-\,71^{7}$	$$	$8.42614977318$		✓	not computed	$D_{7}$ (as 14T2)	trivial	$2$	$6$	$2.56161916129$
14.0.9669040949311.1	x^14 - x^13 + 3x^12 - 6x^11 + 5x^10 - 9x^9 + 11x^8 - 7x^7 + 11x^6 - 9x^5 + 5x^4 - 6x^3 + 3x^2 - x + 1	$14$	[0,7]	$-\,19^{2}\cdot 79\cdot 18413^{2}$	$$	$8.46305933364$			✓	14T57	trivial	$2$	$6$	$2.65828702774$
14.0.9745585291264.1	x^14 - 4x^13 + 7x^12 - 4x^11 - 8x^10 + 24x^9 - 30x^8 + 16x^7 + 13x^6 - 38x^5 + 46x^4 - 36x^3 + 19x^2 - 6x + 1	$14$	[0,7]	$-\,2^{14}\cdot 29^{6}$	$$	$8.467827352511435$			✓	$C_7 \wr C_2$ (as 14T8)	trivial	$4$	$6$	$5.342840135225723$
14.0.9866941650479.1	x^14 - 3x^13 + 6x^12 - 11x^11 + 16x^10 - 21x^9 + 25x^8 - 25x^7 + 25x^6 - 21x^5 + 16x^4 - 11x^3 + 6x^2 - 3x + 1	$14$	[0,7]	$-\,167^{2}\cdot 191\cdot 1361^{2}$	$$	$8.47531594932$			✓	14T57	trivial	$2$	$6$	$2.68866215877$
14.0.11856232199187.1	x^14 - x^13 + x^12 - x^10 - x^9 + x^8 - x^7 - x^6 + 3x^5 - 2x^4 + x^3 + x^2 - x + 1	$14$	[0,7]	$-\,3^{7}\cdot 5421231001$	$$	$8.58723475068$			✓	14T61	trivial	$6$	$6$	$9.0466002324$
14.0.12985240103739.1	x^14 - x^13 + x^12 - 4x^11 + 4x^10 - 2x^9 + 5x^8 - 6x^7 + 2x^6 - 2x^5 + 5x^4 - 2x^3 - x + 1	$14$	[0,7]	$-\,3^{7}\cdot 5937466897$	$$	$8.64320868463$			✓	14T61	trivial	$6$	$6$	$9.5585171283$
14.0.13048447346663.1	x^14 - x^13 + 2x^12 - 2x^11 + 2x^10 - 2x^9 + x^8 - x^7 + x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - x + 1	$14$	[0,7]	$-\,23\cdot 37^{2}\cdot 20357^{2}$	$$	$8.64620704819$			✓	14T57	trivial	$2$	$6$	$3.18798462168$
14.0.13824820988163.1	x^14 - 3x^13 + 8x^12 - 18x^11 + 32x^10 - 52x^9 + 70x^8 - 81x^7 + 82x^6 - 70x^5 + 52x^4 - 31x^3 + 16x^2 - 6x + 1	$14$	[0,7]	$-\,3^{7}\cdot 43^{6}$	$$	$8.681975119007818$			not computed	$C_7 \wr C_2$ (as 14T8)	trivial	$6$	$6$	$9.923787361493524$
14.0.16973485041483.1	x^14 - 2x^13 + 2x^12 - 6x^11 + 8x^10 - 4x^9 + 9x^8 - 11x^7 + 6x^6 - 6x^5 + 5x^4 - 4x^3 + 2x^2 + 1	$14$	[0,7]	$-\,3^{7}\cdot 37^{2}\cdot 2381^{2}$	$$	$8.81015693246$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$11.1445691239$
14.0.22139206005899.1	x^14 - 3x^13 + 4x^12 - 2x^11 + x^10 - 4x^9 + 9x^8 - 11x^7 + 9x^6 - 4x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1	$14$	[0,7]	$-\,59\cdot 593^{2}\cdot 1033^{2}$	$$	$8.97895634588$			✓	14T57	trivial	$2$	$6$	$4.38657959616$
14.0.28466647927227.1	x^14 - x^13 + 2x^12 + 3x^11 - x^10 + 4x^9 + 3x^8 + 2x^7 + 2x^4 - 2x^3 - x^2 + 1	$14$	[0,7]	$-\,3^{7}\cdot 114089^{2}$	$$	$9.14163808258$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$15.4833298742$
14.0.30270895108587.1	x^14 - 4x^13 + 6x^12 - 3x^11 - 6x^10 + 14x^9 - 12x^8 + 2x^7 + 10x^6 - 8x^5 - 3x^4 + x^3 + 7x^2 - 5x + 1	$14$	[0,7]	$-\,3^{7}\cdot 7^{12}$	$$	$9.181853855048184$			not computed	$C_7 \wr C_2$ (as 14T8)	trivial	$6$	$6$	$16.520791850817314$
14.0.51902598731283.1	x^14 - 2x^13 + 3x^12 - 6x^11 + 6x^10 - 4x^9 + 3x^8 + x^7 - x^5 + 3x^4 + 3x^2 + x + 1	$14$	[0,7]	$-\,3^{11}\cdot 17117^{2}$	$$	$9.54237247067$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$27.6082700412$
14.2.52058057626129.1	x^14 - 2x^13 + 3x^12 - 4x^11 + 4x^10 - 4x^9 + 4x^8 - 5x^7 + 4x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - 2x + 1	$14$	[2,6]	$7215127^{2}$	$$	$9.54441116258$			not computed	14T55	trivial	$2$	$7$	$9.48144292717$
14.2.54815765790289.1	x^14 + x^12 - 2x^8 - x^7 - 2x^6 + x^2 + 1	$14$	[2,6]	$7^{2}\cdot 1057681^{2}$	$$	$9.57966653808$			✓	14T55	trivial	$2$	$7$	$9.77968117968$
14.2.55059380046329.1	x^14 - 4x^13 + 6x^12 - x^11 - 10x^10 + 18x^9 - 18x^8 + 15x^7 - 13x^6 + 11x^5 - 8x^4 + 6x^3 - 3x^2 + 1	$14$	[2,6]	$277^{2}\cdot 569\cdot 1123^{2}$	$$	$9.58270130317$			not computed	14T57	trivial	$2$	$7$	$9.77909350979$
14.0.56316949686099.1	x^14 - 2x^13 + 6x^12 - 11x^11 + 19x^10 - 26x^9 + 33x^8 - 35x^7 + 33x^6 - 26x^5 + 19x^4 - 10x^3 + 6x^2 - x + 1	$14$	[0,7]	$-\,3^{7}\cdot 2953^{3}$	$$	$9.59817157113$			✓	$D_7 \wr C_2$ (as 14T20)	trivial	$6$	$6$	$24.3506832156$
14.2.62662828387597.1	x^14 - x^13 - 3x^12 + 5x^11 + 2x^10 - 11x^9 + 4x^8 + 11x^7 - 11x^6 - 2x^5 + 10x^4 - 4x^3 - 2x^2 + 3x - 1	$14$	[2,6]	$167^{2}\cdot 1213\cdot 1361^{2}$	$$	$9.67165316326$			✓	14T57	trivial	$2$	$7$	$10.6313575761$
14.2.63097400703125.1	x^14 - 3x^13 + 2x^12 + 4x^11 - 8x^10 + 2x^9 + 8x^8 - 10x^7 + x^6 + 7x^5 - 6x^4 + x^3 + 2x^2 - x + 1	$14$	[2,6]	$5^{7}\cdot 807646729$	$$	$9.6764287896$			not computed	14T61	trivial	$2$	$7$	$10.6889300961$
14.2.68537510017457.1	x^14 - 4x^13 + 10x^12 - 15x^11 + 11x^10 + 6x^9 - 26x^8 + 35x^7 - 26x^6 + 6x^5 + 11x^4 - 15x^3 + 10x^2 - 4x + 1	$14$	[2,6]	$13^{4}\cdot 17\cdot 109^{4}$	$$	$9.73375911642$			✓	14T51	trivial	$2$	$7$	$11.2548274629$
14.0.74532401109963.1	x^14 - x^13 + 2x^12 - x^11 + 2x^10 - 2x^9 + 2x^8 - 2x^7 - 3x^5 - x^3 + 2x^2 + x + 1	$14$	[0,7]	$-\,3^{7}\cdot 184607^{2}$	$$	$9.79223424158$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$26.6828967522$
14.0.76600746490099.1	x^14 - 2x^13 + 6x^12 - 8x^11 + 16x^10 - 17x^9 + 24x^8 - 21x^7 + 24x^6 - 17x^5 + 16x^4 - 8x^3 + 6x^2 - 2x + 1	$14$	[0,7]	$-\,13^{4}\cdot 19\cdot 109^{4}$	$$	$9.811398801$			not computed	14T51	trivial	$2$	$6$	$9.51678072789$
14.2.78352380449344.1	x^14 - 2x^12 + x^10 + 2x^8 - 3x^6 + x^4 - 1	$14$	[2,6]	$2^{6}\cdot 23^{2}\cdot 73^{2}\cdot 659^{2}$	$$	$9.82725668122$			not computed	14T55	trivial	$2$	$7$	$12.5841466704$
14.2.94241555580481.1	x^14 - x^12 - 2x^9 + 3x^7 - 2x^5 - x^2 + 1	$14$	[2,6]	$43^{2}\cdot 401^{2}\cdot 563^{2}$	$$	$9.95772606431$			✓	14T55	trivial	$2$	$7$	$13.4715273772$
14.2.94724481953125.1	x^14 - x^13 - 2x^12 + 5x^11 + 2x^10 - 9x^9 + 2x^8 + 10x^7 - 6x^6 - 6x^5 + 7x^4 + x^3 - 4x^2 + 1	$14$	[2,6]	$5^{7}\cdot 199\cdot 6092831$	$$	$9.96136219536$			✓	14T61	trivial	$2$	$7$	$13.5893961295$
14.2.103886084489093.1	x^14 - 3x^12 - 3x^11 + 6x^10 + 7x^9 - 5x^8 - 12x^7 + 2x^6 + 11x^5 + x^4 - 7x^3 - 2x^2 + 4x - 1	$14$	[2,6]	$53\cdot 977^{2}\cdot 1433^{2}$	$$	$10.0272690923$			not computed	14T57	trivial	$2$	$7$	$14.647522546$
14.2.116768679686993.1	x^14 - 3x^13 + 7x^12 - 14x^11 + 21x^10 - 29x^9 + 35x^8 - 37x^7 + 35x^6 - 29x^5 + 21x^4 - 14x^3 + 7x^2 - 3x + 1	$14$	[2,6]	$257\cdot 674057^{2}$	$$	$10.1113472722$			✓	14T57	trivial	$2$	$7$	$15.418973911$
14.0.118236562059083.1	x^14 - 3x^13 + 2x^12 + 3x^11 - 5x^10 - x^9 + x^8 + 2x^7 + 11x^6 - 13x^5 + 6x^4 - 8x^3 + 4x^2 + 1	$14$	[0,7]	$-\,13\cdot 71^{7}$	$$	$10.1203738706$			not computed	14T38	trivial	$2$	$6$	$12.9746502268$
14.2.154291569457229.1	x^14 - x^13 + x^12 - 2x^11 + 2x^10 - 3x^9 + 3x^8 - 3x^7 + 3x^6 - 3x^5 + 2x^4 - 2x^3 + x^2 - x + 1	$14$	[2,6]	$29\cdot 107^{2}\cdot 21557^{2}$	$$	$10.3146148047$			✓	14T57	trivial	$2$	$7$	$17.8336574914$
14.2.160805685121205.1	x^14 + x^12 - x^9 - x^8 - x^7 - x^6 - x^5 + x^2 + 1	$14$	[2,6]	$5\cdot 41^{2}\cdot 138319^{2}$	$$	$10.3451267052$			✓	14T57	trivial	$2$	$7$	$20.4518453354$
14.0.172575877556547.1	x^14 - x^13 - x^12 + 2x^10 + x^9 - x^8 - x^7 - x^6 + x^5 + 2x^4 - x^2 - x + 1	$14$	[0,7]	$-\,3^{7}\cdot 280909^{2}$	$$	$10.3974573916$			✓	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$55.4764206676$
14.2.212764932023296.1	x^14 - x^10 + x^8 + x^2 - 1	$14$	[2,6]	$2^{10}\cdot 455827^{2}$	$$	$10.5541055231$			not computed	14T55	trivial	$2$	$7$	$21.4724068698$
14.2.245928712415581.1	x^14 - x^13 + 4x^12 - x^11 + 3x^10 + 3x^9 - 4x^8 + 9x^7 - 16x^6 + 14x^5 - 21x^4 + 10x^3 - 9x^2 + 2x - 1	$14$	[2,6]	$13^{4}\cdot 61\cdot 109^{4}$	$$	$10.6638725375$			not computed	14T51	trivial	$2$	$7$	$26.4300628611$
14.4.250058750499647.1	x^14 - 2x^13 + x^12 - x^11 + x^10 - 4x^9 + 9x^8 - 9x^7 + 9x^6 - 4x^5 + x^4 - x^3 + x^2 - 2x + 1	$14$	[4,5]	$-\,47\cdot 107^{2}\cdot 21557^{2}$	$$	$10.676565665$			✓	14T57	trivial	$2$	$8$	$31.5102502485$
14.0.263657868936003.1	x^14 + x^12 - 2x^11 - x^10 + 3x^7 - x^4 - 2x^3 + x^2 + 1	$14$	[0,7]	$-\,3^{7}\cdot 103^{2}\cdot 3371^{2}$	$$	$10.717027334$			✓	$S_7\times C_2$ (as 14T49)	trivial	$6$	$6$	$73.5044803741$
14.4.270118421833507.1	x^14 - x^13 - 3x^12 - x^11 + x^10 + 2x^8 + 7x^7 + 3x^6 + 4x^5 + 9x^4 + 7x^3 + x^2 + 1	$14$	[4,5]	$-\,13^{4}\cdot 67\cdot 109^{4}$	$$	$10.7355747516$			not computed	14T51	trivial	$2$	$8$	$33.079338429$
14.0.280155320935227.1	x^14 - x^13 + 2x^12 - x^11 + 3x^10 - 4x^9 + 3x^8 - 4x^7 + 2x^6 - 4x^5 + 2x^4 + 5x^2 + 2x + 1	$14$	[0,7]	$-\,3^{7}\cdot 71^{6}$	$$	$10.763587918$			not computed	$D_{14}$ (as 14T3)	trivial	$6$	$6$	$64.9438034848$
14.4.297261105546875.1	x^14 - 3x^12 - x^11 + 5x^10 + 3x^9 - 6x^8 - 6x^7 + 3x^6 + 7x^5 - 4x^3 - 2x^2 + x + 1	$14$	[4,5]	$-\,5^{7}\cdot 89\cdot 971\cdot 44029$	$$	$10.8092504055$			✓	14T61	trivial	$2$	$8$	$34.9413880804$
14.0.318497840669359.1	x^14 - 4x^13 + 8x^12 - 10x^11 + 15x^10 - 28x^9 + 42x^8 - 41x^7 + 32x^6 - 31x^5 + 37x^4 - 35x^3 + 21x^2 - 7x + 1	$14$	[0,7]	$-\,13^{4}\cdot 79\cdot 109^{4}$	$$	$10.8626597908$			not computed	14T51	trivial	$2$	$6$	$22.560872956$
14.2.321952970703125.1	x^14 - 3x^13 + 2x^12 + 3x^11 - 7x^10 + 11x^9 - 25x^8 + 33x^7 - 4x^6 - 56x^5 + 93x^4 - 78x^3 + 38x^2 - 10x + 1	$14$	[2,6]	$5^{9}\cdot 37^{2}\cdot 347^{2}$	$$	$10.8710348587$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$2$	$7$	$30.836203822$
14.4.334624313614643.1	x^14 - x^13 - 4x^12 + 3x^11 + 3x^10 + 3x^9 + 2x^8 - 12x^7 + x^5 + 2x^4 + 6x^3 - 3x^2 + x - 1	$14$	[4,5]	$-\,13^{4}\cdot 83\cdot 109^{4}$	$$	$10.9010515249$			not computed	14T51	trivial	$2$	$8$	$37.8345982696$
14.2.386441371953125.1	x^14 - x^13 - 2x^12 + 4x^11 - 2x^10 - 3x^9 + x^8 + 6x^6 - 11x^5 + 5x^4 - 12x^3 + 24x^2 - 20x + 5	$14$	[2,6]	$5^{7}\cdot 53^{2}\cdot 1327^{2}$	$$	$11.0137330011$			not computed	$S_7\times C_2$ (as 14T49)	trivial	$2$	$7$	$38.0258403894$
14.2.391066968923137.1	x^14 - 4x^13 + 5x^12 + 4x^11 - 14x^10 + 5x^9 + 13x^8 - 9x^7 - 9x^6 + 8x^5 + 4x^4 - 5x^3 + x - 1	$14$	[2,6]	$13^{4}\cdot 97\cdot 109^{4}$	$$	$11.0230975946$			not computed	14T51	trivial	$2$	$7$	$35.8148412318$
14.0.407483719072587.1	x^14 - x^13 + 4x^12 - x^11 + 4x^10 + 2x^9 - 6x^8 + 3x^7 - 6x^6 + 2x^5 + 4x^4 - x^3 + 4x^2 - x + 1	$14$	[0,7]	$-\,3^{15}\cdot 73^{4}$	$$	$11.0555233042$			not computed	$A_7\times C_2$ (as 14T47)	trivial	$6$	$6$	$96.5294199023$
14.4.411650990546875.1	x^14 - 3x^12 - 2x^11 + 5x^10 + 4x^9 - 6x^8 - 7x^7 + 7x^6 + 9x^5 - 4x^4 - 6x^3 + 2x^2 + 2x - 1	$14$	[4,5]	$-\,5^{7}\cdot 24851\cdot 212029$	$$	$11.0635611432$			not computed	14T61	trivial	$2$	$8$	$42.0905477867$
14.2.422859037223221.1	x^14 - 2x^13 - 4x^12 + 6x^11 + 10x^10 - 3x^9 - 19x^8 - 6x^7 + 27x^6 - x^5 - 20x^4 + 9x^3 + 4x^2 - 4x + 1	$14$	[2,6]	$71^{6}\cdot 3301$	$$	$11.0848101244$			not computed	14T38	trivial	$2$	$7$	$32.6924434913$
14.0.445660887761159.1	x^14 - x^13 + 6x^12 - 4x^11 + 12x^10 - 2x^9 + 11x^8 + 3x^7 + 11x^6 - 2x^5 + 12x^4 - 4x^3 + 6x^2 - x + 1	$14$	[0,7]	$-\,7^{2}\cdot 71^{7}$	$$	$11.1264716525$			not computed	14T27	trivial	$2$	$6$	$25.684570553$
14.0.489862582246303.1	x^14 - 5x^13 + 18x^12 - 44x^11 + 89x^10 - 140x^9 + 190x^8 - 209x^7 + 201x^6 - 156x^5 + 104x^4 - 55x^3 + 23x^2 - 7x + 1	$14$	[0,7]	$-\,7^{7}\cdot 29^{6}$	$$	$11.201882659887865$			not computed	$C_7 \wr C_2$ (as 14T8)	trivial	$2$	$6$	$30.78649932175806$
14.2.493856488203125.1	x^14 - 2x^13 + 6x^11 - 3x^10 - 8x^9 + 13x^8 + 4x^7 - 16x^6 + 7x^5 + 13x^4 - 11x^3 - 4x^2 + 6x - 1	$14$	[2,6]	$5^{7}\cdot 43^{6}$	$$	$11.2083816827$			not computed	$D_{14}$ (as 14T3)	trivial	$2$	$7$	$39.9535247267$
14.4.498897726810659.1	x^14 - 2x^13 + 3x^11 - 7x^10 + x^9 + 14x^8 - 2x^7 - 13x^6 + 2x^5 + 4x^4 - 4x^3 + 3x + 1	$14$	[4,5]	$-\,11^{3}\cdot 71^{2}\cdot 8623^{2}$	$$	$11.2165156356$			not computed	14T57	trivial	$2$	$8$	$47.3515916708$