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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
13.13.491258904256726154641.1	x^13 - x^12 - 24x^11 + 19x^10 + 190x^9 - 116x^8 - 601x^7 + 246x^6 + 738x^5 - 215x^4 - 291x^3 + 68x^2 + 10x - 1	\( 53^{12} \)	$C_{13}$ (as 13T1)	Trivial
13.13.59091511031674153381441.1	x^13 - x^12 - 36x^11 + 77x^10 + 365x^9 - 1193x^8 - 617x^7 + 5541x^6 - 4414x^5 - 4575x^4 + 6321x^3 + 411x^2 - 2196x + 293	\( 79^{12} \)	$C_{13}$ (as 13T1)	Trivial
13.13.25542038069936263923006961.1	x^13 - x^12 - 60x^11 + 27x^10 + 1199x^9 - 33x^8 - 9610x^7 - 3352x^6 + 33548x^5 + 20328x^4 - 47723x^3 - 34869x^2 + 21271x + 15667	\( 131^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.224282727500720205065439601.1	x^13 - x^12 - 72x^11 + 129x^10 + 1672x^9 - 3386x^8 - 16810x^7 + 32367x^6 + 81708x^5 - 121902x^4 - 196272x^3 + 127412x^2 + 217458x + 61399	\( 157^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.542800770374370512771595361.1	x^13 - 78x^11 - 65x^10 + 2080x^9 + 2457x^8 - 24128x^7 - 27027x^6 + 137683x^5 + 110214x^4 - 376064x^3 - 128206x^2 + 363883x - 12167	\( 13^{24} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.884162417215006648162206715681.1	x^13 - x^12 - 144x^11 + 161x^10 + 6530x^9 - 9620x^8 - 109398x^7 + 196143x^6 + 512628x^5 - 917970x^4 - 650724x^3 + 1134730x^2 + 253950x - 409375	\( 313^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.57127433662862356193722241010001.1	x^13 - x^12 - 204x^11 - 181x^10 + 10752x^9 + 9116x^8 - 208418x^7 - 161679x^6 + 1686466x^5 + 1207646x^4 - 4904338x^3 - 3051848x^2 + 896956x + 144209	\( 443^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.399993265701109317068886081212641.1	x^13 - x^12 - 240x^11 - 293x^10 + 19153x^9 + 45777x^8 - 616830x^7 - 1795569x^6 + 7791196x^5 + 23224049x^4 - 29107980x^3 - 68466088x^2 + 31673025x + 4516075	\( 521^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.717542973516054083971838830896241.1	x^13 - x^12 - 252x^11 + 1123x^10 + 15626x^9 - 107844x^8 - 204415x^7 + 3094114x^6 - 4853400x^5 - 22393129x^4 + 91453411x^3 - 116380476x^2 + 47088126x - 1165671	\( 547^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.2133643557240451317422184503752801.1	x^13 - x^12 - 276x^11 + 1967x^10 + 8169x^9 - 109375x^8 + 114077x^7 + 1684091x^6 - 4924742x^5 - 5465967x^4 + 34969245x^3 - 20502539x^2 - 55304818x + 57031547	\( 599^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.9269664678331989431355838883693521.1	x^13 - x^12 - 312x^11 + 765x^10 + 31073x^9 - 114643x^8 - 1071164x^7 + 4472586x^6 + 13888428x^5 - 61633266x^4 - 43862553x^3 + 238916059x^2 - 140970591x - 1052321	\( 677^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.161405364891475526005003176560483281.1	x^13 - x^12 - 396x^11 + 1235x^10 + 45719x^9 - 158783x^8 - 2232951x^7 + 7665285x^6 + 47857178x^5 - 162308625x^4 - 381260855x^3 + 1359880245x^2 + 391778734x - 2211739517	\( 859^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.326753707264991140811478515720435521.1	x^13 - x^12 - 420x^11 + 4253x^10 + 2721x^9 - 193733x^8 + 735262x^7 + 31458x^6 - 3569396x^5 + 1482536x^4 + 4833237x^3 + 1733969x^2 - 40719x - 57869	\( 911^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)
13.13.458010137458255714802917980980035681.1	x^13 - x^12 - 432x^11 + 1203x^10 + 46006x^9 - 37046x^8 - 2039413x^7 - 3276218x^6 + 27799988x^5 + 87214801x^4 - 38878963x^3 - 420910202x^2 - 520002704x - 190078187	\( 937^{12} \)	$C_{13}$ (as 13T1)	Trivial (GRH)