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 6 matches)

Label	Polynomial	Discriminant	Galois group	Class group
32.0.24788700386255228556692600250244140625.1	x^32 - 2x^31 + x^29 + 14x^28 - 23x^27 - 25x^26 + 77x^25 + 32x^24 - 233x^23 + 130x^22 + 275x^21 - 204x^20 - 500x^19 + 369x^18 + 976x^17 - 775x^16 - 1988x^15 + 2706x^14 + 1255x^13 - 4074x^12 + 870x^11 + 3435x^10 - 2784x^9 - 528x^8 + 1624x^7 - 465x^6 - 564x^5 + 639x^4 - 293x^3 + 55x^2 - x + 1	\( 5^{28}\cdot 13^{16} \)	$C_8.A_4$ (as 32T402)	Trivial (GRH)
32.0.515207889456069254383620937908064472169867121.1	x^32 - 5x^31 + 22x^30 - 73x^29 + 220x^28 - 519x^27 + 1255x^26 - 2247x^25 + 4413x^24 - 6238x^23 + 9744x^22 - 10830x^21 + 13240x^20 - 10628x^19 + 12053x^18 - 5501x^17 + 12591x^16 - 3062x^15 + 17256x^14 + 194x^13 + 18165x^12 + 5659x^11 + 13232x^10 - 2318x^9 - 319x^8 - 13445x^7 - 6940x^6 - 4990x^5 + 1466x^4 + 2074x^3 + 1626x^2 + 264x + 79	\( 7^{16}\cdot 13^{28} \)	$C_8.A_4$ (as 32T402)	Trivial (GRH)
32.0.2294081869728198830572049522437155246734619140625.1	x^32 - 11x^31 + 68x^30 - 336x^29 + 1315x^28 - 4335x^27 + 12498x^26 - 30713x^25 + 67152x^24 - 127199x^23 + 211471x^22 - 307078x^21 + 387026x^20 - 419617x^19 + 359728x^18 - 149755x^17 - 229142x^16 + 581095x^15 - 441722x^14 - 315448x^13 + 1021466x^12 - 946897x^11 + 366311x^10 - 50246x^9 + 132237x^8 - 215882x^7 + 157773x^6 - 97500x^5 + 79930x^4 - 54894x^3 + 25063x^2 - 7709x + 3131	\( 3^{32}\cdot 5^{28}\cdot 7^{16} \)	$C_8.A_4$ (as 32T402)	Trivial (GRH)
32.0.6142666889587199870339155304469168186187744140625.1	x^32 - 4x^31 + 38x^30 - 130x^29 + 699x^28 - 2191x^27 + 8745x^26 - 25571x^25 + 83386x^24 - 222738x^23 + 612551x^22 - 1445800x^21 + 3366820x^20 - 6839883x^19 + 13440516x^18 - 23161945x^17 + 38310126x^16 - 55684805x^15 + 77474162x^14 - 94829103x^13 + 110710129x^12 - 113727761x^11 + 110357640x^10 - 94103904x^9 + 74479117x^8 - 51698016x^7 + 32429638x^6 - 17496051x^5 + 7973462x^4 - 3036857x^3 + 868340x^2 - 166271x + 16531	\( 5^{28}\cdot 67^{16} \)	$C_8.A_4$ (as 32T402)	Trivial (GRH)
32.0.170615961014359235699341036323165930807590484619140625.1	x^32 - 9x^31 + 200x^29 - 221x^28 - 2631x^27 + 4402x^26 + 19766x^25 - 27449x^24 - 173128x^23 + 338537x^22 + 473336x^21 - 1004401x^20 - 3368948x^19 + 11453717x^18 - 8139429x^17 - 16834230x^16 - 597015x^15 + 195460786x^14 - 382818671x^13 - 27697040x^12 + 420160443x^11 + 1322753872x^10 - 3917503795x^9 + 2111159122x^8 + 2050419221x^7 + 1497324960x^6 - 10922257252x^5 + 11658561303x^4 - 2839464368x^3 - 2153549419x^2 + 711827200x + 313809121	\( 5^{28}\cdot 127^{16} \)	$C_8.A_4$ (as 32T402)	$[3]$ (GRH)
32.0.357097144070652207046431305343854464590549468994140625.1	x^32 + 10x^30 - 34x^29 - 221x^28 - 325x^27 + 1702x^26 + 10506x^25 + 30252x^24 + 14963x^23 - 179369x^22 - 807831x^21 - 1736093x^20 - 816295x^19 + 9325990x^18 + 44064917x^17 + 128084070x^16 + 284677470x^15 + 521805347x^14 + 810649893x^13 + 1086373418x^12 + 1261930239x^11 + 1284857142x^10 + 1126974132x^9 + 881072238x^8 + 561801072x^7 + 341439909x^6 + 154026757x^5 + 83319621x^4 + 32957519x^3 + 18318673x^2 + 5994407x + 1916071	\( 5^{28}\cdot 7^{16}\cdot 19^{16} \)	$C_8.A_4$ (as 32T402)	Trivial (GRH)