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 143)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.117033789351264256.3	x^16 - 6x^15 + 16x^14 - 30x^13 + 60x^12 - 122x^11 + 204x^10 - 304x^9 + 466x^8 - 660x^7 + 742x^6 - 680x^5 + 607x^4 - 540x^3 + 372x^2 - 154x + 29	\( 2^{24}\cdot 17^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.1866675593471230161.1	x^16 - 5x^15 + 8x^14 - 11x^13 + 31x^12 - 34x^11 + 14x^10 - 61x^9 + 76x^8 - 54x^7 + 84x^6 - 24x^5 + 24x^4 - 18x^3 - 9x + 9	\( 3^{12}\cdot 37^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.4611686018427387904.3	x^16 - 8x^15 + 32x^14 - 80x^13 + 144x^12 - 224x^11 + 328x^10 - 432x^9 + 494x^8 - 496x^7 + 456x^6 - 384x^5 + 280x^4 - 160x^3 + 64x^2 - 16x + 2	\( 2^{62} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.4611686018427387904.5	x^16 - 8x^15 + 40x^14 - 136x^13 + 356x^12 - 728x^11 + 1208x^10 - 1624x^9 + 1800x^8 - 1624x^7 + 1192x^6 - 696x^5 + 312x^4 - 104x^3 + 24x^2 - 8x + 5	\( 2^{62} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.101881126126588011921.1	x^16 - 6x^15 + 21x^14 - 45x^13 + 52x^12 - 3x^11 - 123x^10 + 234x^9 - 159x^8 - 174x^7 + 675x^6 - 1167x^5 + 1471x^4 - 1254x^3 + 711x^2 - 210x + 25	\( 3^{12}\cdot 61^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.295147905179352825856.3	x^16 + 8x^14 + 28x^12 + 56x^10 + 74x^8 + 72x^6 + 20x^4 - 40x^2 + 9	\( 2^{68} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.295147905179352825856.5	x^16 - 8x^14 + 28x^12 - 56x^10 + 74x^8 - 72x^6 + 20x^4 + 40x^2 + 9	\( 2^{68} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.864576140260219140625.1	x^16 - x^15 - 3x^14 + 16x^13 - 29x^11 + 136x^10 + 106x^9 - 439x^8 - 393x^7 + 355x^6 + 311x^5 - 185x^4 + 36x^3 + 398x^2 + 259x + 49	\( 5^{8}\cdot 19^{12} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.2555478887462114090409.5	x^16 + 2x^14 + 19x^12 + 215x^10 + 1561x^8 + 5054x^6 + 8179x^4 + 6329x^2 + 1849	\( 3^{12}\cdot 37^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.0.4229909006359687890625.1	x^16 - 8x^15 + 42x^14 - 154x^13 + 440x^12 - 1002x^11 + 1844x^10 - 2752x^9 + 3246x^8 - 2918x^7 + 1975x^6 - 1035x^5 + 483x^4 - 237x^3 + 109x^2 - 34x + 5	\( 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial
16.0.4229909006359687890625.3	x^16 - 8x^15 + 38x^14 - 126x^13 + 321x^12 - 652x^11 + 1115x^10 - 1648x^9 + 2235x^8 - 2792x^7 + 3341x^6 - 3586x^5 + 3608x^4 - 2978x^3 + 2151x^2 - 1020x + 355	\( 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.21614403506505478515625.4	x^16 - 6x^15 + 4x^14 + 60x^13 - 192x^12 + 116x^11 + 540x^10 - 1487x^9 + 2264x^8 - 3856x^7 + 6890x^6 - 7933x^5 + 4783x^4 - 3080x^3 + 6731x^2 - 8087x + 3541	\( 5^{10}\cdot 19^{12} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.0.50787142148496295121281.1	x^16 - 3x^15 + 13x^14 - 43x^13 + 87x^12 - 209x^11 + 532x^10 - 903x^9 + 1142x^8 - 1179x^7 + 1433x^6 - 1172x^5 + 864x^4 - 241x^3 + 140x^2 - 48x + 9	\( 13^{8}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.50787142148496295121281.3	x^16 - 3x^15 + 2x^14 + 4x^13 - 2x^12 + x^11 + 28x^9 + 16x^8 - 77x^7 + 104x^6 + 57x^5 + 34x^4 - 21x^3 + 180x^2 + 216x + 81	\( 13^{8}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.105747725158992197265625.1	x^16 + 9x^14 + 19x^12 + 16x^10 + 35x^8 + 16x^6 + 19x^4 + 9x^2 + 1	\( 5^{10}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.0.156381544652244701169601.2	x^16 - x^15 - x^14 - 7x^13 - 3x^12 + 20x^11 + 128x^10 + 350x^9 + 596x^8 + 1057x^7 + 1434x^6 + 1382x^5 + 1274x^4 + 997x^3 + 478x^2 + 117x + 13	\( 13^{8}\cdot 61^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.156381544652244701169601.4	x^16 + 13x^14 + 71x^12 + 234x^10 + 547x^8 + 910x^6 + 938x^4 + 468x^2 + 81	\( 13^{8}\cdot 61^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.166101760110563345913601.1	x^16 - 3x^15 + 10x^14 - 26x^13 + 11x^12 + 78x^11 - 95x^10 - 154x^9 + 540x^8 - 449x^7 + 25x^6 - 460x^5 + 573x^4 + 29x^3 + 291x^2 - 209x + 51	\( 17^{8}\cdot 47^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[5]$ (GRH)
16.0.379099670317033992358041.5	x^16 - 8x^15 + 32x^14 - 84x^13 + 191x^12 - 418x^11 + 1144x^10 - 2937x^9 + 4567x^8 - 3528x^7 - 4016x^6 + 14875x^5 - 2581x^4 - 19272x^3 + 35864x^2 - 23830x + 53971	\( 3^{12}\cdot 61^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.0.446012924483368791310336.1	x^16 - 2x^14 + 21x^12 - 50x^10 + 356x^8 + 362x^6 + 1893x^4 + 1274x^2 + 2401	\( 2^{24}\cdot 113^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[15]$ (GRH)
16.0.625307362087580183568001.1	x^16 - x^15 - 6x^14 + 14x^13 + 17x^12 - 50x^11 - 41x^10 - 8x^9 + 6x^8 + 71x^7 - 449x^6 + 410x^5 + 2301x^4 + 1587x^3 + 653x^2 - 4921x + 3107	\( 23^{8}\cdot 41^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[3]$ (GRH)
16.0.843842771347424502531361.2	x^16 - 2x^15 + 14x^13 + 13x^12 + 56x^11 + 159x^10 + 340x^9 + 982x^8 + 3130x^7 + 7837x^6 + 13910x^5 + 18208x^4 + 17400x^3 + 12032x^2 + 5600x + 1472	\( 11^{8}\cdot 89^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.861754256028993434290561.1	x^16 - 12x^14 + 28x^12 - 21x^10 + 1064x^8 - 3381x^6 + 1876x^4 - 2420x^2 + 14641	\( 7^{12}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.2643693128974804931640625.16	x^16 - 7x^15 + 11x^14 + 40x^13 - 140x^12 - 82x^11 + 864x^10 - 302x^9 - 2285x^8 + 2650x^7 + 1856x^6 - 8412x^5 + 4416x^4 + 13495x^3 - 12885x^2 - 9400x + 10805	\( 5^{12}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2, 2]$ (GRH)
16.0.2832629623265327154715681.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 56x^12 + 154x^11 - 137x^10 - 107x^9 + 518x^8 - 880x^7 + 1023x^6 - 913x^5 + 725x^4 - 512x^3 + 112x^2 + 72x + 16	\( 17^{8}\cdot 67^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[5]$ (GRH)
16.0.4113758514028199904823761.1	x^16 - 5x^15 + 11x^14 + 13x^13 - 72x^12 + 154x^11 - 25x^10 - 171x^9 + 1583x^8 - 1528x^7 - 953x^6 + 6684x^5 - 73x^4 + 1625x^3 + 8110x^2 + 496x + 269	\( 3^{4}\cdot 13^{8}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2]$ (GRH)
16.0.6810271162553824314519361.1	x^16 - 8x^15 + 24x^14 - 28x^13 + 102x^12 - 612x^11 + 1852x^10 - 3364x^9 + 3849x^8 - 2516x^7 + 628x^6 + 144x^5 + 851x^4 - 1830x^3 + 433x^2 + 474x + 67	\( 31^{8}\cdot 41^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[3]$ (GRH)
16.0.7136206791733900660965376.1	x^16 + 23x^14 + 200x^12 + 835x^10 + 1757x^8 + 1824x^6 + 852x^4 + 140x^2 + 4	\( 2^{28}\cdot 113^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[7]$ (GRH)
16.0.8583027023095873875496489.7	x^16 - 8x^15 + 46x^14 - 182x^13 + 625x^12 - 1748x^11 + 4521x^10 - 9966x^9 + 20478x^8 - 35624x^7 + 56302x^6 - 72839x^5 + 81644x^4 - 70111x^3 + 47477x^2 - 20616x + 5463	\( 13^{10}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2]$ (GRH)
16.0.11023665190835148548573041.2	x^16 - 5x^15 + 21x^14 - 64x^13 + 193x^12 - 630x^11 + 1539x^10 - 3879x^9 + 6842x^8 - 9035x^7 + 16285x^6 - 10912x^5 + 21963x^4 - 9330x^3 + 20571x^2 + 575x + 13225	\( 11^{12}\cdot 37^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2]$ (GRH)
16.0.17876432388376151935981441.1	x^16 - 9x^14 + 114x^12 - 444x^10 + 2099x^8 + 2853x^6 + 17403x^4 + 27078x^2 + 94249	\( 13^{8}\cdot 23^{12} \)	$C_2^2.SD_{16}$ (as 16T163)	$[3]$ (GRH)
16.0.26428481046229354497662569.5	x^16 - 3x^15 - x^14 + 19x^13 - 47x^12 + 21x^11 + 93x^10 - 121x^9 + 184x^8 - 404x^7 + 115x^6 + 431x^5 - 140x^4 - 2061x^3 + 5706x^2 - 5805x + 2025	\( 13^{10}\cdot 61^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.8.27752432990725912250390625.1	x^16 - 3x^14 - 91x^12 + 237x^10 + 1721x^8 - 6120x^6 + 4090x^4 + 675x^2 + 25	\( 3^{8}\cdot 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.8.27752432990725912250390625.2	x^16 - x^15 - 16x^14 + 11x^13 + 53x^12 - 258x^11 - 112x^10 + 975x^9 + 1660x^8 + 1662x^7 - 3679x^6 - 6784x^5 - 2461x^4 + 2633x^3 + 9313x^2 + 683x - 1817	\( 3^{8}\cdot 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.43149301773875176172265625.8	x^16 - 4x^15 + 25x^14 - 90x^13 + 318x^12 - 766x^11 + 2331x^10 - 4110x^9 + 9186x^8 - 15286x^7 + 23043x^6 - 27690x^5 + 47385x^4 - 13369x^3 + 57891x^2 + 3015x + 23395	\( 5^{8}\cdot 101^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2]$ (GRH)
16.0.48003408671952806969030689.1	x^16 + 21x^14 + 231x^12 + 482x^10 + 199x^8 + 46x^6 + 258x^4 - 28x^2 + 1	\( 17^{10}\cdot 47^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2, 10]$ (GRH)
16.16.114179308667742410575446016.1	x^16 - 4x^15 - 34x^14 + 148x^13 + 311x^12 - 1596x^11 - 906x^10 + 6856x^9 + 357x^8 - 13240x^7 + 1452x^6 + 11384x^5 - 740x^4 - 3792x^3 - 352x^2 + 48x + 4	\( 2^{32}\cdot 113^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.142661082295126092995678329.1	x^16 - x^15 + 19x^14 - 63x^13 + 222x^12 - 697x^11 + 1948x^10 - 6018x^9 + 14623x^8 - 26850x^7 + 40454x^6 - 49012x^5 + 50677x^4 - 43130x^3 + 18971x^2 - 546x + 9	\( 13^{8}\cdot 53^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)
16.0.195397579112879711966327281.1	x^16 - x^15 + 27x^14 - 21x^13 + 373x^12 - 417x^11 + 2998x^10 - 2924x^9 + 9324x^8 - 10479x^7 + 13730x^6 - 39988x^5 + 27154x^4 + 108305x^3 + 215491x^2 + 133159x + 42529	\( 11^{12}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.277211316640788505600000000.1	x^16 - 9x^14 + 194x^12 + 74x^10 - 1230x^8 + 265x^6 + 5000x^4 - 2275x^2 + 625	\( 2^{16}\cdot 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[16]$ (GRH)
16.0.277211316640788505600000000.2	x^16 + x^14 + 31x^12 + 527x^10 + 4629x^8 + 32926x^6 + 120089x^4 + 204020x^2 + 255025	\( 2^{16}\cdot 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[36]$ (GRH)
16.0.277211316640788505600000000.3	x^16 + 9x^14 + 194x^12 - 74x^10 - 1230x^8 - 265x^6 + 5000x^4 + 2275x^2 + 625	\( 2^{16}\cdot 5^{8}\cdot 101^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[10]$ (GRH)
16.16.456717234670969642301784064.1	x^16 - 23x^14 + 200x^12 - 835x^10 + 1757x^8 - 1824x^6 + 852x^4 - 140x^2 + 4	\( 2^{34}\cdot 113^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	Trivial (GRH)
16.0.581895727651002533052085321.5	x^16 - 4x^15 + 5x^14 + 25x^13 - 308x^12 + 1165x^11 - 1271x^10 - 4714x^9 + 27762x^8 - 73079x^7 + 123062x^6 - 144991x^5 + 127502x^4 - 86543x^3 + 43670x^2 - 14196x + 2197	\( 13^{8}\cdot 61^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2]$ (GRH)
16.0.694998991499817467531640625.1	x^16 - 2x^14 + 21x^12 - 487x^10 + 1730x^8 - 40997x^6 + 165759x^4 + 473993x^2 + 1172889	\( 5^{8}\cdot 59^{12} \)	$C_2^2.SD_{16}$ (as 16T163)	$[3]$ (GRH)
16.0.818629961123679547712831809.5	x^16 - 2x^15 - 6x^14 + 13x^13 - 32x^12 + 32x^11 + 195x^10 + 50x^9 + 140x^8 - 2121x^7 + 2844x^6 - 6816x^5 + 2791x^4 + 6234x^3 + 37680x^2 - 96560x + 69904	\( 17^{10}\cdot 67^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2, 2]$ (GRH)
16.0.1051141675669222288577809681.2	x^16 + 5x^14 + 83x^12 + 370x^10 + 2535x^8 + 9358x^6 + 20846x^4 - 6808x^2 + 529	\( 23^{8}\cdot 41^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2, 6]$ (GRH)
16.0.1172430065629619555264631841.1	x^16 - 2x^15 - 7x^14 + 25x^13 + 9x^12 - 149x^11 - 3x^10 + 624x^9 - 270x^8 - 2114x^7 + 1503x^6 + 6250x^5 + 215x^4 - 9923x^3 + 377x^2 - 391x + 3871	\( 41^{8}\cdot 59^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[3]$ (GRH)
16.0.1450531566903202684958906641.12	x^16 + 5x^14 - 25x^12 + 54x^10 + 3099x^8 + 25098x^6 + 70814x^4 + 76916x^2 + 25281	\( 13^{12}\cdot 53^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[2, 2]$ (GRH)
16.0.2420667705185442556922185849.5	x^16 + 27x^14 + 306x^12 + 3960x^10 + 42647x^8 + 178205x^6 + 591167x^4 + 1204062x^2 + 5248681	\( 7^{12}\cdot 53^{10} \)	$C_2^2.SD_{16}$ (as 16T163)	$[4]$ (GRH)