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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.5.35351257235385344.1	x^15 - 3x^13 - 5x^12 + 8x^11 + x^10 + 14x^9 - 13x^8 - 17x^7 + 4x^6 + x^5 + 22x^4 - 2x^3 - 8x^2 - 3x - 1	\( -\,2^{10}\cdot 11^{13} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.5.388863829589238784.1	x^15 - 3x^14 + 2x^13 - x^12 + 5x^11 - 22x^9 + 33x^8 - 22x^7 + 22x^6 - 22x^5 - 9x^4 + 38x^3 - 29x^2 + 9x - 1	\( -\,2^{10}\cdot 11^{14} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.5.20200001513509571303.1	x^15 - x^14 - 4x^13 + 7x^12 + 24x^11 - 26x^10 - 57x^9 + 76x^8 + 79x^7 - 88x^6 - 97x^5 + 35x^4 + 42x^3 - 15x^2 + 1	\( -\,11^{12}\cdot 23^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial
15.15.140998454960622300613.1	x^15 - 6x^14 - 3x^13 + 80x^12 - 96x^11 - 330x^10 + 715x^9 + 308x^8 - 1694x^7 + 715x^6 + 1287x^5 - 1217x^4 + 53x^3 + 263x^2 - 76x + 1	\( 11^{14}\cdot 13^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial (GRH)
15.15.539190459461999816537.1	x^15 - x^14 - 23x^13 + 2x^12 + 169x^11 + 66x^10 - 473x^9 - 264x^8 + 572x^7 + 341x^6 - 297x^5 - 157x^4 + 69x^3 + 25x^2 - 6x - 1	\( 11^{14}\cdot 17^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial (GRH)
15.5.337135860780576171875000000000000000.1	x^15 - 110x^13 - 330x^12 + 6050x^11 + 25674x^10 - 442200x^9 - 2425610x^8 + 6912345x^7 + 36375350x^6 - 70930618x^5 - 40668100x^4 + 762404060x^3 - 1733605720x^2 - 2315335000x + 7384846832	\( -\,2^{15}\cdot 5^{25}\cdot 11^{13} \)	$S_3 \times C_5$ (as 15T4)	$[5, 5]$ (GRH)
15.15.183165087243372408306736095370388796571648.1	x^15 - 676x^13 - 2038x^12 + 154340x^11 + 777118x^10 - 13426470x^9 - 81228726x^8 + 443602723x^7 + 3071208794x^6 - 3528834550x^5 - 35037744764x^4 - 10574547144x^3 + 113736612400x^2 + 132200896640x + 34747476224	\( 2^{15}\cdot 11^{13}\cdot 61^{13} \)	$S_3 \times C_5$ (as 15T4)	$[5]$ (GRH)
15.5.330059514666048497176686804227168786358108620765840999.1	x^15 - 2x^14 - 5995x^13 + 37278x^12 + 12591603x^11 - 125770086x^10 - 9981552889x^9 + 127789199194x^8 + 1679913052736x^7 - 14585961566768x^6 - 215344958988368x^5 + 7140439214752x^4 + 11110764946271360x^3 + 74237750960369664x^2 + 322453908130652160x + 543122152076214272	\( -\,11^{12}\cdot 19^{5}\cdot 461^{13} \)	$S_3 \times C_5$ (as 15T4)	$[2, 2, 10, 8125610]$ (GRH)
15.15.2368379989452191012928309708195070432434082031250000000000.1	x^15 - 11275x^13 - 124025x^12 + 45081960x^11 + 891723965x^10 - 76578988200x^9 - 2216106307965x^8 + 44485161759555x^7 + 2079870790777010x^6 + 8195553887899983x^5 - 457716480374582000x^4 - 5640651315561778120x^3 + 1700941616424112590x^2 + 316610688507343605265x + 1257096395450004601701	\( 2^{10}\cdot 3^{5}\cdot 5^{25}\cdot 11^{13}\cdot 41^{13} \)	$S_3 \times C_5$ (as 15T4)	$[5, 5, 55]$ (GRH)
15.5.218974301248546884855355633871639977128201417943833178401792.1	x^15 - 2x^14 - 5518x^13 + 145177x^12 + 10337726x^11 - 586917623x^10 + 3771529909x^9 + 531822012342x^8 - 23558245878420x^7 + 579004818046875x^6 - 10215903964721319x^5 + 131630106918356613x^4 - 1205008059400695846x^3 + 5950390757960217555x^2 + 20744208523450960470x - 156585180055842346293	\( -\,2^{10}\cdot 3^{5}\cdot 11^{5}\cdot 31^{13}\cdot 181^{13} \)	$S_3 \times C_5$ (as 15T4)	n/a
15.5.41175521478048478091458686420635252885332273019437320881692114944.1	x^15 - 2x^14 - 32683x^13 + 474556x^12 + 398483171x^11 - 9448930490x^10 - 2149890958601x^9 + 60044615624016x^8 + 4866594417860856x^7 - 97851943474667568x^6 - 5825118141734624712x^5 + 17888510070027150336x^4 + 3008732613506684865072x^3 + 35886037118520058343136x^2 + 505655319767204772863856x + 5751424233849962588258304	\( -\,2^{15}\cdot 3^{5}\cdot 11^{13}\cdot 41^{13}\cdot 61^{13} \)	$S_3 \times C_5$ (as 15T4)	n/a