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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.12.1406010138282259297589421.1	x^16 - x^15 - 21x^14 + 4x^13 + 150x^12 + 62x^11 - 250x^10 + 29x^9 - 985x^8 - 3787x^7 + 778x^6 + 12561x^5 + 11101x^4 - 5392x^3 - 13007x^2 - 6933x - 1227	\( 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.4.1406010138282259297589421.1	x^16 - 7x^15 + 32x^14 - 90x^13 + 177x^12 - 132x^11 - 366x^10 + 1732x^9 - 3832x^8 + 5737x^7 - 6188x^6 + 4581x^5 - 4588x^4 + 1860x^3 - 1387x^2 + 80x + 149	\( 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.8.1406010138282259297589421.1	x^16 - 3x^15 + 2x^14 + 12x^13 - 27x^12 - 44x^11 + 22x^10 + 104x^9 - 410x^8 - 579x^7 + 1130x^6 + 211x^5 - 1581x^4 + 2680x^3 + 4591x^2 + 891x - 453	\( 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.8.1406010138282259297589421.2	x^16 - 8x^15 + 22x^14 - 7x^13 - 74x^12 + 155x^11 - 230x^10 + 306x^9 - 46x^8 - 492x^7 + 922x^6 - 1278x^5 + 1019x^4 + 349x^3 - 1520x^2 + 943x - 163	\( 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.2.120225114802785897280700416.3	x^16 - 6x^15 + 23x^14 - 118x^13 + 456x^12 - 924x^11 + 3492x^10 - 9532x^9 + 5553x^8 - 33142x^7 + 82411x^6 + 174240x^5 + 220821x^4 - 276410x^3 - 2521242x^2 - 3309980x - 5229262	\( -\,2^{18}\cdot 2777^{6} \)	16T1674	$[2]$ (GRH)
16.2.120225114802785897280700416.4	x^16 - 6x^15 + 9x^14 + 76x^13 - 389x^12 + 866x^11 + 1579x^10 - 10704x^9 + 22073x^8 - 45354x^7 + 49469x^6 - 22790x^5 - 152066x^4 + 1211476x^3 - 2500989x^2 + 2267208x - 957101	\( -\,2^{18}\cdot 2777^{6} \)	16T1674	$[2]$ (GRH)
16.0.245343529829932519644987392.1	x^16 + 16x^12 + 88x^8 + 184x^4 + 92	\( 2^{56}\cdot 23^{7} \)	16T1674	$[2]$ (GRH)
16.4.245343529829932519644987392.1	x^16 + 24x^12 + 424x^8 - 920x^4 + 92	\( 2^{56}\cdot 23^{7} \)	16T1674	Trivial (GRH)
16.12.507569659919895606429780981.1	x^16 - 4x^15 - 19x^14 + 112x^13 - 1087x^11 + 1975x^10 + 3276x^9 - 14246x^8 + 7437x^7 + 32541x^6 - 52434x^5 - 6192x^4 + 65205x^3 - 35586x^2 - 3159x + 729	\( 3^{5}\cdot 19^{8}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.4.507569659919895606429780981.1	x^16 - 5x^15 + 21x^14 - 91x^13 + 324x^12 - 976x^11 + 2128x^10 - 3121x^9 - 2260x^8 + 17593x^7 - 48673x^6 + 85037x^5 - 70596x^4 - 7443x^3 + 31326x^2 + 31543x + 27103	\( 3^{5}\cdot 19^{8}\cdot 103^{7} \)	16T1674	$[2]$ (GRH)
16.6.1923601836844574356491206656.3	x^16 - 6x^15 + 20x^14 - 158x^13 + 60x^12 - 1010x^11 - 1282x^10 + 3370x^9 - 6781x^8 + 62938x^7 + 60070x^6 + 232778x^5 + 478345x^4 + 247862x^3 + 698774x^2 + 61168x - 76012	\( -\,2^{22}\cdot 2777^{6} \)	16T1674	$[2]$ (GRH)
16.6.1923601836844574356491206656.4	x^16 - 6x^15 - 2x^14 + 176x^13 - 762x^12 - 1148x^11 + 13080x^10 - 6288x^9 - 88060x^8 + 96648x^7 + 317368x^6 - 440080x^5 - 713816x^4 + 950992x^3 + 1176352x^2 - 898080x - 1193888	\( -\,2^{22}\cdot 2777^{6} \)	16T1674	$[2]$ (GRH)
16.0.92144280422466145326820294656.1	x^16 + 76x^14 + 2221x^12 + 32743x^10 + 265216x^8 + 1188208x^6 + 2773893x^4 + 2888532x^2 + 1003941	\( 2^{16}\cdot 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	$[2, 2, 2452]$ (GRH)
16.16.92144280422466145326820294656.1	x^16 - 86x^14 + 2902x^12 - 49411x^10 + 453495x^8 - 2216251x^6 + 5273394x^4 - 4825962x^2 + 1003941	\( 2^{16}\cdot 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.0.92144280422466145326820294656.2	x^16 + 86x^14 + 2902x^12 + 49411x^10 + 453495x^8 + 2216251x^6 + 5273394x^4 + 4825962x^2 + 1003941	\( 2^{16}\cdot 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	$[2, 2, 2996]$ (GRH)
16.16.92144280422466145326820294656.2	x^16 - 76x^14 + 2221x^12 - 32743x^10 + 265216x^8 - 1188208x^6 + 2773893x^4 - 2888532x^2 + 1003941	\( 2^{16}\cdot 3^{5}\cdot 19^{6}\cdot 103^{7} \)	16T1674	Trivial (GRH)
16.4.6329643282720100095594349789184.3	x^16 + 38x^14 - 3878x^12 - 95067x^10 + 5170588x^8 + 85763937x^6 - 3234288019x^4 - 40931317670x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1674	$[2]$ (GRH)
16.0.68657178731138146229972916764672.1	x^16 - 368x^12 - 8648x^8 + 21121912x^4 + 25745372	\( 2^{56}\cdot 23^{11} \)	16T1674	$[2, 2]$ (GRH)