Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.304011857053427966889939263171547.1	x^22 - x^21 + 11x^20 - 8x^19 + 73x^18 - 46x^17 + 301x^16 - 145x^15 + 883x^14 - 355x^13 + 1776x^12 - 498x^11 + 2527x^10 - 574x^9 + 2324x^8 - 251x^7 + 1358x^6 - 161x^5 + 400x^4 + 20x^3 + 51x^2 - 6x + 1	\( -\,3^{11}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[23]$ (GRH)
22.0.328417397709776899721953240383603.1	x^22 - 2x^21 + 14x^20 - 22x^19 + 110x^18 - 154x^17 + 537x^16 - 588x^15 + 1719x^14 - 1556x^13 + 3922x^12 - 2650x^11 + 6120x^10 - 3124x^9 + 6945x^8 - 2284x^7 + 4957x^6 - 987x^5 + 2301x^4 - 102x^3 + 153x^2 + 9	\( -\,3^{15}\cdot 4784137656827^{2} \)	22T47	$[16]$ (GRH)
22.0.420249828754162766851850612806803.1	x^22 - 3x^21 + 17x^20 - 32x^19 + 133x^18 - 221x^17 + 675x^16 - 925x^15 + 2270x^14 - 2774x^13 + 5421x^12 - 5457x^11 + 8435x^10 - 7261x^9 + 8780x^8 - 5447x^7 + 4182x^6 - 1619x^5 + 1047x^4 - 323x^3 + 152x^2 - 13x + 1	\( -\,3^{11}\cdot 421^{2}\cdot 115692385433^{2} \)	22T47	$[28]$ (GRH)
22.0.7198079267989980836471065337135104.1	x^22 + 21x^20 + 190x^18 + 969x^16 + 3060x^14 + 6188x^12 + 8008x^10 + 6435x^8 + 3003x^6 + 715x^4 + 66x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[67]$ (GRH)
22.2.18498813244074511635519301831008736129.1	x^22 - 2x^21 + 16x^20 + 12x^19 - 55x^18 + 482x^17 - 2477x^16 + 1764x^15 - 26905x^14 - 8523x^13 - 179279x^12 - 129306x^11 - 552925x^10 - 120476x^9 - 752931x^8 + 162572x^7 - 958963x^6 + 202039x^5 - 1129686x^4 + 1534908x^3 - 1835434x^2 + 973620x - 247433	\( 23^{20}\cdot 47^{6} \)	22T23	$[2, 2, 2, 4]$ (GRH)
22.0.20375776275370821024303050129100543619.1	x^22 - 11x^21 + 90x^20 - 515x^19 + 2404x^18 - 9153x^17 + 29609x^16 - 81730x^15 + 195276x^14 - 404718x^13 + 730608x^12 - 1147506x^11 + 1565057x^10 - 1843981x^9 + 1862690x^8 - 1595475x^7 + 1141091x^6 - 667142x^5 + 309476x^4 - 109065x^3 + 27307x^2 - 4313x + 323	\( -\,19^{11}\cdot 211^{10} \)	$D_{22}$ (as 22T3)	$[23]$ (GRH)
22.0.168778618179498920541003256266493001728.1	x^22 - 88x^11 + 2048	\( -\,2^{20}\cdot 7^{11}\cdot 11^{22} \)	$C_2\times F_{11}$ (as 22T6)	$[22]$ (GRH)
22.0.222623423334106740048017938136372833267.1	x^22 - x^21 + 2x^20 + 40x^19 - 33x^18 + 59x^17 + 535x^16 - 361x^15 + 574x^14 + 2902x^13 - 1439x^12 + 2088x^11 + 6412x^10 - 3927x^9 + 3984x^8 + 2341x^7 - 9804x^6 + 3508x^5 + 355x^4 - 5700x^3 + 5006x^2 + 186x + 1073	\( -\,67^{21} \)	$C_{22}$ (as 22T1)	$[67]$ (GRH)
22.0.265223542853498303707290831275917574144.1	x^22 - 11x^21 + 44x^20 - 33x^19 - 264x^18 + 495x^17 + 1331x^16 - 5698x^15 + 3619x^14 + 13915x^13 + 14498x^12 - 61939x^11 - 78386x^10 + 27313x^9 + 373593x^8 - 284306x^7 + 237369x^6 - 11385x^5 + 47520x^4 + 99x^3 + 4334x^2 - 913x + 45	\( -\,2^{20}\cdot 7^{10}\cdot 11^{23} \)	$C_2\times F_{11}$ (as 22T6)	$[22]$ (GRH)
22.0.45838394542255573972509544658660888671875.1	x^22 - x^21 + 21x^20 - 40x^19 + 325x^18 - 597x^17 + 2667x^16 - 4827x^15 + 15510x^14 - 22580x^13 + 42773x^12 - 36183x^11 + 50648x^10 - 29240x^9 + 42285x^8 - 15537x^7 + 18462x^6 - 4332x^5 + 5605x^4 - 760x^3 + 441x^2 + 44x + 16	\( -\,3^{21}\cdot 5^{20}\cdot 11^{16} \)	$C_2\times C_{11}:C_5$ (as 22T5)	$[93]$ (GRH)
22.2.6320614583435223575185822515817648777854976.1	x^22 + 55x^20 + 1177x^18 + 12639x^16 + 73898x^14 + 237402x^12 + 390258x^10 + 246906x^8 - 33011x^6 - 40249x^4 - 451x^2 - 1	\( 2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T34	$[20]$ (GRH)
22.2.34222877449943760059204182577145233543266304.1	x^22 + 94x^20 + 2826x^18 + 37945x^16 + 251867x^14 + 761654x^12 + 230402x^10 - 4536140x^8 - 11307192x^6 - 11114418x^4 - 4607953x^2 - 605699	\( 2^{22}\cdot 467\cdot 1297^{11} \)	22T32	$[12]$ (GRH)
22.6.1833841138186726138360895488000000000000000000000.1	x^22 + 55x^20 + 165x^18 - 25025x^16 - 276485x^14 + 2066735x^12 + 43231375x^10 + 184328485x^8 + 61775780x^6 - 734883710x^4 - 983938615x^2 - 240015655	\( 2^{32}\cdot 5^{21}\cdot 11^{23} \)	22T37	$[2, 2, 4]$ (GRH)
22.2.42678484670527444674580840448000000000000000000000.2	x^22 + 55x^20 + 495x^18 - 17985x^16 - 433675x^14 - 3686375x^12 - 14668500x^10 - 29976650x^8 - 32599875x^6 - 18319125x^4 - 4728625x^2 - 435125	\( 2^{40}\cdot 5^{21}\cdot 11^{22} \)	22T37	$[2, 14]$ (GRH)
22.2.309044195601903421945287518629445365867259019395072.1	x^22 + 101x^20 + 4176x^18 + 91407x^16 + 1138432x^14 + 8015565x^12 + 29342566x^10 + 41164011x^8 - 37023993x^6 - 171064312x^4 - 170043296x^2 - 54560547	\( 2^{22}\cdot 74843^{9} \)	22T42	$[90]$ (GRH)
22.2.69060143384057543649123162895045349831909332275390625.1	x^22 + 44x^20 - 704x^18 - 1694x^17 + 5489x^16 - 181016x^15 - 321409x^14 + 1107876x^13 - 11311036x^12 + 24054074x^11 + 268019961x^10 + 590825576x^9 + 7709668824x^8 - 18265694150x^7 + 68368497131x^6 + 222554589730x^5 - 308868066991x^4 + 45202657280x^3 - 20879387045x^2 + 107908541730x + 10858117145	\( 5^{16}\cdot 11^{40} \)	$C_{11}:D_{11}.C_2$ (as 22T8)	$[11]$ (GRH)
22.22.15511205137931876981971247794361198940089877934973874833.1	x^22 - 11x^21 - 99x^20 + 1309x^19 + 3047x^18 - 60159x^17 - 16577x^16 + 1390774x^15 - 844338x^14 - 17555384x^13 + 17916371x^12 + 121098216x^11 - 147077084x^10 - 422212637x^9 + 569624253x^8 + 585528031x^7 - 974902588x^6 - 50899365x^5 + 524533735x^4 - 271848962x^3 + 57376176x^2 - 5011721x + 110603	\( 11^{40}\cdot 17^{11} \)	$C_{22}$ (as 22T1)	$[23]$ (GRH)