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 1314)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.1156440847592456192.1	x^15 - 7x^14 + 29x^13 - 83x^12 + 185x^11 - 323x^10 + 445x^9 - 463x^8 + 341x^7 - 143x^6 + 3x^5 + 35x^4 - 15x^3 + x^2 + 3x - 1	\( -\,2^{23}\cdot 13^{10} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.2678296388369907712.1	x^15 - 6x^13 - 6x^12 + 8x^9 + 24x^8 + 22x^7 - 16x^5 - 28x^4 - 42x^3 - 40x^2 - 20x - 4	\( -\,2^{37}\cdot 11^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.6400000000000000000.1	x^15 - 5x^14 + 15x^13 - 35x^12 + 65x^11 - 93x^10 + 125x^9 - 125x^8 + 115x^7 - 55x^6 + 43x^5 + 5x^4 + 15x^3 + 5x^2 + 5x - 1	\( -\,2^{23}\cdot 5^{17} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.3.189863754266000000000.1	x^15 - x^14 + 3x^13 - 14x^12 + 10x^11 - 36x^10 + 57x^9 - 44x^8 + 60x^7 - 77x^6 - 63x^5 + 6x^4 - 66x^3 - 67x^2 - 18x - 1	\( 2^{10}\cdot 5^{9}\cdot 37^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.968890104070000000000.1	x^15 - 2x^14 - x^13 - 6x^12 + 28x^11 - 21x^10 - 21x^9 + 32x^8 + 62x^7 - 151x^6 + 60x^5 + 56x^4 - 42x^3 - 7x^2 + 21x + 7	\( -\,2^{10}\cdot 5^{10}\cdot 7^{13} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.1245564843750000000000.1	x^15 - 33x^10 + 363x^5 - 81	\( -\,2^{10}\cdot 3^{13}\cdot 5^{17} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.3.1254970340000000000000.1	x^15 - 3x^14 - x^13 + 25x^12 - 29x^11 - 77x^10 + 173x^9 + 101x^8 - 505x^7 - 61x^6 + 915x^5 - 67x^4 - 719x^3 + 65x^2 - 181x + 221	\( 2^{14}\cdot 5^{13}\cdot 13^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.5.2058857500000000000000.1	x^15 - 10x^13 + 10x^11 - 74x^10 - 90x^9 + 50x^8 - 80x^7 - 160x^6 + 124x^5 + 140x^4 - 60x^3 - 60x^2 + 4	\( -\,2^{14}\cdot 5^{16}\cdot 7^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.5.2573571875000000000000.1	x^15 - 5x^13 - 5x^12 - 20x^11 - 10x^10 + 30x^9 + 70x^8 + 95x^7 + 110x^6 + 85x^5 + 185x^4 + 45x^3 + 50x^2 - 25x - 5	\( -\,2^{12}\cdot 5^{17}\cdot 7^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.7174453500000000000000.1	x^15 - 2	\( -\,2^{14}\cdot 3^{15}\cdot 5^{15} \)	$F_5 \times S_3$ (as 15T11)	Trivial
15.1.89365537375000000000000.1	x^15 - 20x^10 + 208x^5 + 8	\( -\,2^{12}\cdot 5^{15}\cdot 59^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.164089192000000000000000.1	x^15 - 10x^10 + 22x^5 + 16	\( -\,2^{18}\cdot 5^{15}\cdot 29^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.633881344000000000000000.1	x^15 - 12x^10 + 122x^5 - 16	\( -\,2^{23}\cdot 5^{15}\cdot 19^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.2094432902981048583984375.1	x^15 - 3	\( -\,3^{29}\cdot 5^{15} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.15.11527956194382420421735424.1	x^15 - 7x^14 - 17x^13 + 228x^12 - 217x^11 - 2256x^10 + 5392x^9 + 5898x^8 - 30661x^7 + 17242x^6 + 46052x^5 - 67465x^4 + 22925x^3 + 4610x^2 - 1755x - 169	\( 2^{10}\cdot 17^{9}\cdot 37^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.19007343354618214927734375.1	x^15 - 7	\( -\,3^{15}\cdot 5^{9}\cdot 7^{14} \)	$F_5 \times S_3$ (as 15T11)	$[3]$ (GRH)
15.3.24616451192000000000000000.1	x^15 - 58x^10 - 1006x^5 + 512	\( 2^{18}\cdot 5^{15}\cdot 79^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.41121891520593750000000000.1	x^15 - 60x^10 + 432x^5 - 864	\( -\,2^{10}\cdot 3^{12}\cdot 5^{15}\cdot 19^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.1078834754497843750000000000.1	x^15 - 11x^10 + 2541x^5 + 1331	\( -\,2^{10}\cdot 5^{15}\cdot 11^{13} \)	$F_5 \times S_3$ (as 15T11)	$[5]$ (GRH)
15.1.1859072658893875000000000000.1	x^15 - 80x^10 + 1276x^5 - 262144	\( -\,2^{12}\cdot 5^{15}\cdot 431^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.2672692202031612396240234375.1	x^15 - 5	\( -\,3^{15}\cdot 5^{29} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.2828100578830827520000000000.1	x^15 - 4x^14 + 16x^13 - 108x^12 + 278x^11 - 672x^10 + 2556x^9 - 3184x^8 + 5212x^7 - 4832x^6 + 4940x^5 - 2112x^4 + 2728x^3 + 176x^2 + 704x + 176	\( -\,2^{23}\cdot 5^{10}\cdot 11^{13} \)	$F_5 \times S_3$ (as 15T11)	$[5]$ (GRH)
15.1.3974609857841055286000000000.1	x^15 - 77x^10 + 3927x^5 - 2401	\( -\,2^{10}\cdot 5^{9}\cdot 7^{13}\cdot 29^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.15.4079123598546500000000000000.1	x^15 - 30x^13 + 300x^11 - 24x^10 - 1300x^9 + 190x^8 + 2500x^7 - 380x^6 - 2046x^5 + 300x^4 + 570x^3 - 100x^2 - 20x + 2	\( 2^{14}\cdot 5^{15}\cdot 7^{6}\cdot 37^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.4962305746407473152000000000.1	x^15 - 5x^13 - 10x^12 + 10x^11 - 38x^10 + 30x^9 - 450x^8 - 4795x^7 - 560x^6 + 1367x^5 - 13630x^4 + 12520x^3 - 37650x^2 + 3820x - 24862	\( -\,2^{23}\cdot 5^{9}\cdot 13^{13} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.5772256435841343750000000000.1	x^15 - 147x^10 - 183x^5 - 81	\( -\,2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 41^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.20096697792256000000000000000.1	x^15 - 92x^10 + 3314x^5 - 50000	\( -\,2^{23}\cdot 5^{15}\cdot 151^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.34315188682441500000000000000.1	x^15 - 6	\( -\,2^{14}\cdot 3^{29}\cdot 5^{15} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.42356520216086413824000000000.1	x^15 - x^14 - 32x^13 - 2x^12 + 419x^11 + 403x^10 - 948x^9 + 858x^8 - 4068x^7 - 34920x^6 + 17076x^5 + 151848x^4 - 33552x^3 - 257256x^2 + 198540x - 43596	\( -\,2^{18}\cdot 3^{13}\cdot 5^{9}\cdot 139^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.51353462694600000000000000000.1	x^15 - 366x^10 + 61152x^5 - 5038848	\( -\,2^{18}\cdot 3^{13}\cdot 5^{17}\cdot 11^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.144306410896033593750000000000.1	x^15 - 5x^14 + 5x^13 - 120x^12 + 250x^11 + 650x^10 + 4235x^9 - 2970x^8 - 11100x^7 - 38665x^6 + 40325x^5 + 89950x^4 + 145530x^3 - 162925x^2 - 120050x - 84035	\( -\,2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 41^{5} \)	$F_5 \times S_3$ (as 15T11)	$[3]$ (GRH)
15.1.184712205946923000000000000000.1	x^15 - 30x^10 + 183x^5 + 2592	\( -\,2^{15}\cdot 3^{13}\cdot 5^{15}\cdot 41^{5} \)	$F_5 \times S_3$ (as 15T11)	$[2]$ (GRH)
15.3.236621177025197656250000000000.1	x^15 - 637x^10 + 23673x^5 + 28561	\( 2^{10}\cdot 5^{17}\cdot 13^{13} \)	$F_5 \times S_3$ (as 15T11)	$[4]$ (GRH)
15.1.302875106592253000000000000000.1	x^15 - 117x^10 + 65x^5 - 28561	\( -\,2^{15}\cdot 5^{15}\cdot 13^{13} \)	$F_5 \times S_3$ (as 15T11)	$[2, 4]$ (GRH)
15.1.547770268742400000000000000000.1	x^15 - 25x^13 - 50x^12 + 250x^11 + 964x^10 - 250x^9 - 8400x^8 - 22675x^7 + 9000x^6 + 63307x^5 - 78250x^4 - 120600x^3 - 150700x^2 - 319000x - 250228	\( -\,2^{23}\cdot 3^{12}\cdot 5^{17}\cdot 11^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.582452128062025000000000000000.1	x^15 - 5x^14 + 20x^13 - 40x^12 + 65x^11 + 18x^10 - 160x^9 + 40x^8 - 2380x^7 + 6930x^6 - 6267x^5 + 15095x^4 - 24230x^3 + 33910x^2 - 15635x + 2216	\( -\,2^{15}\cdot 5^{17}\cdot 13^{12} \)	$F_5 \times S_3$ (as 15T11)	$[4]$ (GRH)
15.1.669849889354556129280000000000.1	x^15 - x^14 + 38x^13 - 46x^12 + 723x^11 - 1429x^10 + 7038x^9 - 17686x^8 + 61012x^7 - 68704x^6 + 255224x^5 - 170052x^4 + 243720x^3 + 1864080x^2 + 992796x + 158700	\( -\,2^{23}\cdot 3^{12}\cdot 5^{10}\cdot 109^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.750034830013451205120000000000.1	x^15 - 3x^14 + 3x^13 - 37x^12 + 33x^11 - 915x^10 + 2935x^9 - 2409x^8 + 15195x^7 + 81103x^6 + 72609x^5 + 486393x^4 + 747683x^3 + 1597287x^2 + 1440165x + 4559605	\( -\,2^{18}\cdot 3^{13}\cdot 5^{10}\cdot 179^{5} \)	$F_5 \times S_3$ (as 15T11)	$[5]$ (GRH)
15.1.789540317195400000000000000000.1	x^15 - 5x^14 - 15x^13 + 15x^12 + 525x^11 - 1173x^10 - 1665x^9 + 2265x^8 + 55335x^7 - 96635x^6 + 356773x^5 + 792135x^4 + 666495x^3 + 3088125x^2 + 6149115x + 6561729	\( -\,2^{18}\cdot 3^{13}\cdot 5^{17}\cdot 19^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.3.1007749819250299256832000000000.1	x^15 - 3984x^10 - 576882x^5 - 104976	\( 2^{23}\cdot 3^{13}\cdot 5^{9}\cdot 131^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.1092115440368652343750000000000.1	x^15 - 75x^10 + 1505x^5 - 625	\( -\,2^{10}\cdot 5^{28}\cdot 31^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.3051899536187545593750000000000.1	x^15 - 20x^13 - 30x^12 + 160x^11 + 471x^10 - 280x^9 - 3060x^8 - 4660x^7 + 4560x^6 + 15203x^5 - 3060x^4 - 21600x^3 - 27060x^2 - 28440x - 14451	\( -\,2^{10}\cdot 3^{12}\cdot 5^{15}\cdot 179^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.8371557531424512000000000000000.1	x^15 - 288x^10 + 45630x^5 - 34992	\( -\,2^{23}\cdot 3^{13}\cdot 5^{15}\cdot 29^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.3.8989138598669915625000000000000.1	x^15 - 5x^14 + 85x^13 - 385x^12 + 2195x^11 - 6493x^10 + 16875x^9 - 30705x^8 + 22635x^7 - 101775x^6 + 243723x^5 + 262305x^4 - 411255x^3 - 419175x^2 - 901395x - 231831	\( 2^{12}\cdot 3^{13}\cdot 5^{17}\cdot 71^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.9128822781954600000000000000000.1	x^15 - 5x^14 - 30x^13 + 60x^12 + 765x^11 + 561x^10 - 8220x^9 - 26970x^8 + 4440x^7 + 238660x^6 + 420532x^5 - 403920x^4 - 1831320x^3 - 3816360x^2 - 4945740x - 2381172	\( -\,2^{18}\cdot 3^{13}\cdot 5^{17}\cdot 31^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.11684893160901888000000000000000.1	x^15 - 84x^10 + 2526x^5 - 1296	\( -\,2^{23}\cdot 3^{13}\cdot 5^{15}\cdot 31^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.3.15330693091321490625000000000000.1	x^15 - 5x^14 + 95x^13 - 270x^12 + 2665x^11 - 4825x^10 + 34115x^9 - 44010x^8 + 177525x^7 - 261205x^6 + 418175x^5 - 439550x^4 + 133680x^3 + 14000x^2 - 215600x + 54880	\( 2^{12}\cdot 3^{13}\cdot 5^{17}\cdot 79^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.29997949942318842441880000000000.1	x^15 - 5x^14 - 15x^13 + 140x^12 - 95x^11 - 1273x^10 + 3015x^9 + 6270x^8 - 49345x^7 + 84935x^6 - 32349x^5 + 143020x^4 - 328340x^3 + 382390x^2 - 154970x + 364550	\( -\,2^{12}\cdot 5^{10}\cdot 13^{13}\cdot 19^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.50328437500000000000000000000000.1	x^15 - 100x^10 + 11010x^5 + 10000	\( -\,2^{23}\cdot 5^{28}\cdot 11^{5} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.1.71593606587568261546872000000000.1	x^15 - x^14 + 38x^13 - 76x^12 + 747x^11 - 2533x^10 + 9150x^9 - 32728x^8 + 116212x^7 - 210208x^6 + 705164x^5 - 1043136x^4 + 2362896x^3 + 646344x^2 - 610356x + 106644	\( -\,2^{12}\cdot 3^{12}\cdot 5^{9}\cdot 1759^{5} \)	$F_5 \times S_3$ (as 15T11)	$[2]$ (GRH)