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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
13.13.50359924122392641.1	x^13 - 2x^12 - 11x^11 + 23x^10 + 39x^9 - 91x^8 - 44x^7 + 145x^6 - 6x^5 - 89x^4 + 29x^3 + 14x^2 - 8x + 1	\( 50359924122392641 \)	$S_{13}$ (as 13T9)	Trivial
13.13.74057741281094693.1	x^13 - 3x^12 - 8x^11 + 27x^10 + 22x^9 - 89x^8 - 23x^7 + 132x^6 + 5x^5 - 87x^4 + 4x^3 + 21x^2 - 2x - 1	\( 74057741281094693 \)	$S_{13}$ (as 13T9)	Trivial
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
13.13.145952577189773202214912.1	x^13 - 26x^11 + 260x^9 - 1248x^7 + 2912x^5 - 2912x^3 + 832x - 176	\( 2^{12}\cdot 7^{6}\cdot 13^{13} \)	$F_{13}$ (as 13T6)	Trivial
13.13.282638808125771304198601.1	x^13 - 3x^12 - 41x^11 + 155x^10 + 376x^9 - 2028x^8 - 13x^7 + 8927x^6 - 7711x^5 - 13367x^4 + 20364x^3 + 1404x^2 - 13408x + 5312	\( 8101^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
13.13.353629668200918277880881.1	x^13 - 39x^11 + 507x^9 - 156x^8 - 2925x^7 + 1872x^6 + 7605x^5 - 7488x^4 - 6435x^3 + 10062x^2 - 2691x - 306	\( 3^{12}\cdot 13^{16} \)	$C_{13}:C_3$ (as 13T3)	Trivial
13.13.361712403654141025034641.1	x^13 - x^12 - 50x^11 + 25x^10 + 722x^9 - 226x^8 - 4207x^7 + 1158x^6 + 10465x^5 - 2535x^4 - 9399x^3 + 1079x^2 + 1316x - 49	\( 23^{6}\cdot 367^{6} \)	$D_{13}$ (as 13T2)	Trivial (GRH)
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)
13.13.302875106592253000000000000.1	x^13 - 65x^11 + 1625x^9 - 19500x^7 + 113750x^5 - 284375x^3 + 203125x - 69500	\( 2^{12}\cdot 5^{12}\cdot 13^{13} \)	$F_{13}$ (as 13T6)	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)
13.13.9109989259587930139892578125.1	x^13 - 130x^11 - 390x^10 + 3900x^9 + 21255x^8 + 10985x^7 - 119145x^6 - 213785x^5 + 106470x^4 + 499395x^3 + 197730x^2 - 296595x - 205335	\( 3^{6}\cdot 5^{12}\cdot 13^{15} \)	$C_{13}:C_4$ (as 13T4)	Trivial (GRH)
13.13.56748517752373669031468765184.1	x^13 - 117x^11 - 26x^10 + 3692x^9 + 2938x^8 - 38987x^7 - 54314x^6 + 137670x^5 + 290524x^4 - 5824x^3 - 298948x^2 - 169403x - 13406	\( 2^{12}\cdot 3^{6}\cdot 13^{20} \)	$C_{13}:C_6$ (as 13T5)	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)
13.13.1706902865139206151939937338729.1	x^13 - 78x^11 + 1989x^9 - 1326x^8 - 21255x^7 + 33813x^6 + 68328x^5 - 216723x^4 + 191178x^3 - 51948x^2 - 5850x + 1875	\( 3^{12}\cdot 13^{22} \)	$C_{13}:C_6$ (as 13T5)	Trivial (GRH)
13.13.11623368434110587434575082172853.1	x^13 - 91x^11 - 26x^10 + 2951x^9 + 1339x^8 - 41431x^7 - 25922x^6 + 234988x^5 + 213772x^4 - 406770x^3 - 373113x^2 + 223587x + 170991	\( 13^{21}\cdot 19^{6} \)	$C_{13}:C_4$ (as 13T4)	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)
13.13.362838554526023011241407675367424.1	x^13 - 214x^11 - 528x^10 + 15084x^9 + 63024x^8 - 390420x^7 - 2357568x^6 + 2053638x^5 + 30420288x^4 + 30740796x^3 - 108639936x^2 - 240370524x - 132080544	\( 2^{36}\cdot 3^{16}\cdot 13^{6}\cdot 71^{4} \)	$\PSL(3,3)$ (as 13T7)	Trivial (GRH)
13.13.362838554526023011241407675367424.2	x^13 - 222x^11 - 64x^10 + 18444x^9 + 14832x^8 - 723404x^7 - 1021200x^6 + 13437870x^5 + 27216624x^4 - 96770628x^3 - 257555808x^2 + 34006548x + 256489920	\( 2^{36}\cdot 3^{16}\cdot 13^{6}\cdot 71^{4} \)	$\PSL(3,3)$ (as 13T7)	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)
13.13.30876721812776703244552125405887603759765625.1	x^13 - 2x^12 - 306x^11 + 737x^10 + 35420x^9 - 94473x^8 - 1919784x^7 + 5276958x^6 + 48766779x^5 - 126847180x^4 - 502327474x^3 + 1061716068x^2 + 1350962689x - 1362894158	\( 3^{28}\cdot 5^{18}\cdot 29^{12} \)	$A_{13}$ (as 13T8)	Trivial (GRH)