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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.366701096059015266304.1	x^16 - 8x^15 + 20x^14 - 70x^12 + 56x^11 + 112x^10 - 120x^9 - 127x^8 + 128x^7 + 108x^6 - 72x^5 - 60x^4 + 16x^3 + 16x^2 - 2	\( 2^{56}\cdot 7\cdot 727 \)	16T1643	Trivial (GRH)
16.2.1348237643948903890944.1	x^16 - 12x^14 + 54x^12 - 108x^10 + 87x^8 - 48x^7 + 108x^6 - 144x^5 + 54x^4 - 3	\( -\,2^{32}\cdot 3^{15}\cdot 131\cdot 167 \)	16T1643	Trivial
16.2.1348237643948903890944.2	x^16 - 8x^15 + 36x^14 - 112x^13 + 266x^12 - 504x^11 + 784x^10 - 1016x^9 + 1113x^8 - 1040x^7 + 844x^6 - 600x^5 + 380x^4 - 208x^3 + 96x^2 - 32x + 4	\( -\,2^{32}\cdot 3^{15}\cdot 131\cdot 167 \)	16T1643	Trivial
16.0.1466804384236061065216.1	x^16 + 4x^14 - 8x^13 + 20x^12 - 72x^11 + 124x^10 - 96x^9 - 24x^8 + 160x^7 - 116x^6 + 40x^5 + 52x^4 - 24x^3 + 20x^2 + 1	\( 2^{58}\cdot 7\cdot 727 \)	16T1643	$[2]$ (GRH)
16.4.1497118007554931640625.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 30x^12 + 2x^11 - 12x^10 - 6x^9 + 18x^8 - 14x^7 + 13x^6 - 19x^5 + 9x^4 + 9x^3 - 13x^2 + 6x + 1	\( 5^{13}\cdot 19^{6}\cdot 131\cdot 199 \)	16T1643	Trivial (GRH)
16.0.7341466322985837133824.1	x^16 + 16x^14 + 112x^12 + 448x^10 + 1126x^8 + 1840x^6 + 1936x^4 + 1216x^2 + 349	\( 2^{42}\cdot 3^{14}\cdot 349 \)	16T1643	$[2]$
16.12.15808771774087158203125.1	x^16 - x^15 - 11x^14 + 5x^13 + 18x^12 - 17x^11 + 78x^10 - 23x^9 - 318x^8 + 249x^7 + 457x^6 - 370x^5 - 285x^4 + 136x^3 + 35x^2 - 14x + 1	\( 5^{12}\cdot 61\cdot 101^{6} \)	16T1643	Trivial (GRH)
16.4.15808771774087158203125.1	x^16 - 8x^15 + 41x^14 - 147x^13 + 386x^12 - 769x^11 + 1109x^10 - 1046x^9 + 252x^8 + 1099x^7 - 2226x^6 + 2411x^5 - 1614x^4 + 618x^3 - 69x^2 - 38x + 11	\( 5^{12}\cdot 61\cdot 101^{6} \)	16T1643	Trivial (GRH)
16.8.15808771774087158203125.1	x^16 - 6x^15 + 2x^14 + 52x^13 - 95x^12 - 87x^11 + 347x^10 - 79x^9 - 484x^8 + 325x^7 + 230x^6 - 320x^5 + 85x^4 + 175x^3 - 50x^2 + 25	\( 5^{12}\cdot 61\cdot 101^{6} \)	16T1643	Trivial (GRH)
16.8.15808771774087158203125.2	x^16 - 44x^12 + 5x^10 + 416x^8 - 125x^6 - 579x^4 - 30x^2 + 61	\( 5^{12}\cdot 61\cdot 101^{6} \)	16T1643	Trivial (GRH)
16.10.51572878410546630859375.1	x^16 - 3x^15 - 8x^14 + 42x^13 - 27x^12 - 178x^11 + 385x^10 + 65x^9 - 1004x^8 + 1020x^7 + 575x^6 - 1383x^5 + 518x^4 + 412x^3 - 343x^2 + 52x + 1	\( -\,5^{12}\cdot 101^{6}\cdot 199 \)	16T1643	Trivial (GRH)
16.6.51572878410546630859375.1	x^16 - 4x^15 + 10x^14 - 20x^13 + 4x^12 + 56x^11 - 208x^10 + 225x^9 + 81x^8 - 584x^7 + 592x^6 + 97x^5 - 506x^4 + 212x^3 + 41x^2 + 63x - 59	\( -\,5^{12}\cdot 101^{6}\cdot 199 \)	16T1643	Trivial (GRH)
16.10.51572878410546630859375.2	x^16 - 2x^15 - 3x^14 - 11x^13 + 42x^12 + 94x^11 - 287x^10 + 27x^9 + 225x^8 + 11x^7 + 39x^6 - 216x^5 + 48x^4 + 69x^3 - 25x^2 - 2x + 1	\( -\,5^{12}\cdot 101^{6}\cdot 199 \)	16T1643	Trivial (GRH)
16.6.51572878410546630859375.2	x^16 - 4x^15 + 9x^14 - 19x^13 + 25x^12 - 49x^11 + 37x^10 + 48x^9 - 22x^8 + 8x^7 - 168x^6 + 12x^5 + 194x^4 - 8x^3 - 62x^2 + 2x + 1	\( -\,5^{12}\cdot 101^{6}\cdot 199 \)	16T1643	Trivial (GRH)
16.12.804262633949149425303552.1	x^16 - 8x^15 + 20x^14 - 94x^12 + 200x^11 - 104x^10 - 360x^9 + 721x^8 - 240x^7 - 620x^6 + 808x^5 - 196x^4 - 336x^3 + 272x^2 - 64x + 4	\( 2^{32}\cdot 3^{12}\cdot 13^{6}\cdot 73 \)	16T1643	Trivial (GRH)
16.4.12688742210345595947265625.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 252x^12 - 420x^11 + 480x^10 - 266x^9 - 272x^8 + 924x^7 - 1315x^6 + 1229x^5 - 779x^4 + 315x^3 - 55x^2 - 10x + 5	\( 5^{12}\cdot 11\cdot 101^{6}\cdot 4451 \)	16T1643	Trivial (GRH)
16.8.21537507840746119384765625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 56x^12 + 28x^11 - 192x^10 + 322x^9 - 278x^8 + 60x^7 + 137x^6 - 159x^5 + 62x^4 + 13x^3 - 19x^2 + 5x + 1	\( 5^{13}\cdot 11\cdot 101^{6}\cdot 1511 \)	16T1643	Trivial (GRH)
16.4.58824439771378315673828125.1	x^16 - 7x^15 + 17x^14 - 10x^13 - 9x^12 + 15x^11 - 92x^10 + 449x^9 - 1764x^8 + 3110x^7 - 690x^6 + 675x^5 - 3915x^4 - 7800x^3 + 6650x^2 - 7850x + 3025	\( 5^{12}\cdot 61^{3}\cdot 101^{6} \)	16T1643	$[2]$ (GRH)
16.14.124098826147989303104372736.1	x^16 - 16x^14 + 88x^12 - 160x^10 - 194x^8 + 1040x^6 - 1160x^4 + 416x^2 - 11	\( -\,2^{42}\cdot 3^{12}\cdot 11\cdot 13^{6} \)	16T1643	Trivial (GRH)
16.2.124098826147989303104372736.1	x^16 + 16x^14 + 88x^12 + 160x^10 - 194x^8 - 1040x^6 - 1160x^4 - 416x^2 - 11	\( -\,2^{42}\cdot 3^{12}\cdot 11\cdot 13^{6} \)	16T1643	$[2]$ (GRH)
16.6.245304095500947330655322112.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 254x^12 - 432x^11 + 532x^10 - 416x^9 + 57x^8 + 376x^7 - 608x^6 + 528x^5 - 268x^4 + 56x^3 + 12x^2 - 8x + 1	\( -\,2^{54}\cdot 3^{15}\cdot 13\cdot 73 \)	16T1643	$[2]$ (GRH)
16.14.304797007207295677490234375.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 168x^12 - 84x^11 + 648x^10 - 182x^9 - 1130x^8 + 684x^7 + 929x^6 - 799x^5 - 272x^4 + 441x^3 - 25x^2 - 103x + 11	\( -\,5^{13}\cdot 29\cdot 101^{6}\cdot 8111 \)	16T1643	Trivial (GRH)
16.10.526094932665986181396484375.1	x^16 - 7x^15 + 2x^14 + 120x^13 - 419x^12 + 135x^11 + 2278x^10 - 4066x^9 - 5154x^8 + 19365x^7 - 305x^6 - 39305x^5 + 19360x^4 + 26450x^3 - 16850x^2 + 625x + 25	\( -\,5^{12}\cdot 101^{8}\cdot 199 \)	16T1643	$[2]$ (GRH)
16.6.526094932665986181396484375.1	x^16 - 4x^15 + 2x^14 - 17x^13 - 84x^12 + 379x^11 - 33x^10 + 1529x^9 + 2357x^8 - 3325x^7 - 1892x^6 - 12888x^5 - 33858x^4 - 19866x^3 - 19601x^2 + 82340x - 30469	\( -\,5^{12}\cdot 101^{8}\cdot 199 \)	16T1643	$[2]$ (GRH)
16.10.526094932665986181396484375.2	x^16 - 21x^14 - 11x^13 + 152x^12 + 197x^11 - 872x^10 + 1690x^9 - 4023x^8 - 2006x^7 + 16092x^6 - 16391x^5 + 3386x^4 + 15663x^3 - 20233x^2 + 6246x - 319	\( -\,5^{12}\cdot 101^{8}\cdot 199 \)	16T1643	$[2]$ (GRH)
16.10.2042337557936057128662109375.1	x^16 - x^15 - 23x^14 - 10x^13 + 295x^12 + 411x^11 - 2519x^10 - 4960x^9 + 9379x^8 + 23980x^7 - 3661x^6 - 29037x^5 - 13815x^4 - 21410x^3 - 33317x^2 - 13933x - 1709	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	Trivial (GRH)
16.2.2042337557936057128662109375.1	x^16 - 4x^15 + 21x^14 - 106x^13 + 382x^12 - 486x^11 - 2439x^10 + 17312x^9 - 58866x^8 + 134892x^7 - 220262x^6 + 253015x^5 - 189354x^4 + 72485x^3 + 7540x^2 - 19705x + 7655	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	$[2, 2]$ (GRH)
16.6.2042337557936057128662109375.1	x^16 - 19x^14 - 70x^13 - 203x^12 - 410x^11 + 1673x^10 + 13050x^9 + 47045x^8 + 125525x^7 + 230492x^6 + 226775x^5 + 88497x^4 + 83485x^3 + 184269x^2 + 120130x + 22081	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	$[2]$ (GRH)
16.10.2042337557936057128662109375.2	x^16 - 3x^15 - 31x^14 + 157x^13 - 3x^12 - 1602x^11 + 4319x^10 - 3114x^9 - 7536x^8 + 40819x^7 - 96878x^6 + 112270x^5 - 86079x^4 + 27005x^3 + 68930x^2 - 45255x + 6655	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	Trivial (GRH)
16.6.2042337557936057128662109375.2	x^16 - 4x^15 + x^14 - 36x^13 - 28x^12 + 144x^11 + 386x^10 + 1397x^9 + 1564x^8 + 367x^7 + 43x^6 + 640x^5 + 1701x^4 + 1695x^3 + 2325x^2 + 2020x + 505	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	$[2]$ (GRH)
16.10.2042337557936057128662109375.3	x^16 - 3x^15 + 12x^14 + 8x^13 - 188x^12 + 230x^11 - 382x^10 - 746x^9 + 6370x^8 - 1999x^7 - 10812x^6 + 255x^5 + 5927x^4 + 2777x^3 + 1047x^2 + 433x + 71	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	Trivial (GRH)
16.6.2042337557936057128662109375.3	x^16 - 5x^15 + 3x^14 + 10x^13 - 105x^12 + 475x^11 - 1077x^10 + 3500x^9 - 7461x^8 + 15490x^7 - 27628x^6 + 29560x^5 - 23520x^4 + 14400x^3 - 4928x^2 - 640x + 256	\( -\,5^{12}\cdot 101^{6}\cdot 199^{3} \)	16T1643	Trivial (GRH)
16.10.4235049842663352018394939392.1	x^16 - 96x^12 + 312x^10 + 342x^8 - 1296x^6 + 264x^4 + 840x^2 - 363	\( -\,2^{68}\cdot 3^{15} \)	16T1643	Trivial (GRH)
16.6.4235049842663352018394939392.1	x^16 - 84x^12 - 144x^10 + 1098x^8 + 1584x^6 - 348x^4 - 192x^2 - 3	\( -\,2^{68}\cdot 3^{15} \)	16T1643	Trivial (GRH)
16.8.22524300516639788950855090176.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 242x^12 - 360x^11 + 280x^10 + 184x^9 - 927x^8 + 1504x^7 - 1340x^6 + 504x^5 + 284x^4 - 496x^3 + 144x^2 + 64x + 4	\( 2^{32}\cdot 3^{14}\cdot 11\cdot 13^{6}\cdot 107\cdot 193 \)	16T1643	Trivial (GRH)
16.16.40560270557315574502197265625.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 196x^12 - 644x^11 + 1488x^10 + 2086x^9 - 5336x^8 - 4548x^7 + 10349x^6 + 7341x^5 - 10327x^4 - 7949x^3 + 3629x^2 + 3998x + 781	\( 5^{12}\cdot 101^{6}\cdot 156506561 \)	16T1643	Trivial (GRH)
16.0.54028116220247342960621912064.1	x^16 + 16x^14 + 136x^12 + 736x^10 + 2686x^8 + 6640x^6 + 10792x^4 + 10528x^2 + 4789	\( 2^{42}\cdot 3^{12}\cdot 13^{6}\cdot 4789 \)	16T1643	$[2, 2]$ (GRH)
16.0.54028116220247342960621912064.2	x^16 - 16x^14 + 136x^12 - 736x^10 + 2686x^8 - 6640x^6 + 10792x^4 - 10528x^2 + 4789	\( 2^{42}\cdot 3^{12}\cdot 13^{6}\cdot 4789 \)	16T1643	$[2, 2]$ (GRH)
16.4.129437859287735424258056640625.1	x^16 - 2x^15 - 2x^14 - 88x^13 + 307x^12 - 593x^11 + 354x^10 + 16694x^9 - 125888x^8 + 614113x^7 - 2303824x^6 + 6693031x^5 - 14631028x^4 + 22858964x^3 - 24111593x^2 + 15294944x - 4113659	\( 5^{12}\cdot 11\cdot 101^{8}\cdot 4451 \)	16T1643	$[2]$ (GRH)
16.16.7936557935548946873705350299648.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 194x^12 - 656x^11 + 1492x^10 + 2176x^9 - 5447x^8 - 4776x^7 + 10752x^6 + 7440x^5 - 10956x^4 - 7368x^3 + 4332x^2 + 3096x + 33	\( 2^{54}\cdot 3^{14}\cdot 92111713 \)	16T1643	Trivial (GRH)
16.0.2658157891244233490576000000000000.1	x^16 + 104x^14 + 4508x^12 + 106200x^10 + 1480966x^8 + 12428760x^6 + 60637212x^4 + 154910568x^2 + 156506561	\( 2^{16}\cdot 5^{12}\cdot 101^{6}\cdot 156506561 \)	16T1643	$[2, 8, 18432]$ (GRH)
16.8.30417192973888736937325752197265625.1	x^16 - 2x^15 + 38x^14 - 123x^13 + 207x^12 - 1108x^11 - 51646x^10 + 116979x^9 - 581363x^8 - 1596582x^7 + 13887186x^6 + 3385851x^5 + 27981317x^4 + 105176879x^3 - 927639173x^2 - 564236981x + 2658144721	\( 5^{12}\cdot 11^{3}\cdot 101^{6}\cdot 4451^{3} \)	16T1643	Trivial (GRH)
16.8.30417192973888736937325752197265625.2	x^16 - x^15 - 94x^14 + 165x^13 - 126x^12 - 8447x^11 + 74882x^10 + 474192x^9 + 2077146x^8 - 24295974x^7 - 51262919x^6 + 345170910x^5 - 377718884x^4 - 339713070x^3 + 7219747165x^2 - 10291908080x + 5972069905	\( 5^{12}\cdot 11^{3}\cdot 101^{6}\cdot 4451^{3} \)	16T1643	Trivial (GRH)
16.0.27115868648582425837365776000000000000.1	x^16 + 466x^14 + 88673x^12 + 8834825x^10 + 490769716x^8 + 14941870635x^6 + 228116949332x^4 + 1425939962652x^2 + 1596523428761	\( 2^{16}\cdot 5^{12}\cdot 101^{8}\cdot 156506561 \)	16T1643	$[2, 2, 4, 2693200]$ (GRH)