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
17.17.160470643909878751793805444097921.1	x^17 - x^16 - 48x^15 + 105x^14 + 763x^13 - 2579x^12 - 3653x^11 + 23311x^10 - 11031x^9 - 74838x^8 + 107759x^7 + 50288x^6 - 198615x^5 + 102976x^4 + 58507x^3 - 75722x^2 + 25763x - 2837	\( 103^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.15400296222263289476715621650663041.1	x^17 - x^16 - 64x^15 + 43x^14 + 1478x^13 - 932x^12 - 16008x^11 + 12183x^10 + 86347x^9 - 84507x^8 - 213223x^7 + 271237x^6 + 152800x^5 - 314540x^4 + 100605x^3 + 20132x^2 - 13981x + 1681	\( 137^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.113335617496346216833223278514633468161.1	x^17 - x^16 - 112x^15 + 47x^14 + 3976x^13 - 4314x^12 - 64388x^11 + 136247x^10 + 422013x^9 - 1631073x^8 + 411840x^7 + 5840196x^6 - 11894369x^5 + 10635750x^4 - 4739804x^3 + 938485x^2 - 54850x + 619	\( 239^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.2367911594760467245844106297320951247361.1	x^17 - 136x^15 - 85x^14 + 6154x^13 + 6545x^12 - 119680x^11 - 168555x^10 + 998835x^9 + 1749300x^8 - 2783546x^7 - 6581040x^6 - 678725x^5 + 3813882x^4 + 770593x^3 - 616267x^2 - 82620x + 577	\( 17^{32} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.6226070121392010397563990173530787496001.1	x^17 - x^16 - 144x^15 + 241x^14 + 6894x^13 - 14938x^12 - 127923x^11 + 323969x^10 + 847982x^9 - 2194186x^8 - 2617873x^7 + 6091397x^6 + 3745755x^5 - 7069429x^4 - 1600190x^3 + 3100257x^2 - 220118x - 208777	\( 307^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.613158747081871736694796283376344205805441.1	x^17 - x^16 - 192x^15 + 273x^14 + 14752x^13 - 28028x^12 - 571107x^11 + 1411675x^10 + 11275657x^9 - 36814399x^8 - 91832077x^7 + 461179352x^6 - 109192148x^5 - 1929139488x^4 + 3679722325x^3 - 2767754010x^2 + 828153361x - 45886883	\( 409^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.2200187128095499475530336818113367454680001.1	x^17 - x^16 - 208x^15 - 17x^14 + 15287x^13 + 13881x^12 - 487578x^11 - 703261x^10 + 6754359x^9 + 10540902x^8 - 41136753x^7 - 57683825x^6 + 92010954x^5 + 95287840x^4 - 17501435x^3 - 25026156x^2 - 563260x + 1246103	\( 443^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.397527879693854754943959770157821268619247041.1	x^17 - x^16 - 288x^15 + 265x^14 + 26034x^13 - 40228x^12 - 875968x^11 + 2022008x^10 + 8464009x^9 - 27681440x^8 - 8855367x^7 + 101412811x^6 - 87313302x^5 - 38624139x^4 + 67164168x^3 - 7149746x^2 - 7878215x - 664471	\( 613^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.942906198449660107953222334097149309547713921.1	x^17 - x^16 - 304x^15 + 1117x^14 + 25631x^13 - 126439x^12 - 773932x^11 + 4360454x^10 + 10731832x^9 - 64676368x^8 - 79260104x^7 + 441919082x^6 + 345306489x^5 - 1259087517x^4 - 718017711x^3 + 1025767171x^2 + 183044979x - 202031659	\( 647^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.258850007664814362506653464185428842369437873281.1	x^17 - x^16 - 432x^15 + 1911x^14 + 56071x^13 - 377127x^12 - 2275999x^11 + 22947072x^10 - 5751373x^9 - 395586237x^8 + 1094097337x^7 - 39485017x^6 - 2920148551x^5 + 2341974035x^4 + 1284864535x^3 - 1464500037x^2 - 140787928x + 238840843	\( 919^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)
17.17.462899178676311160288470191817767102492054133121.1	x^17 - x^16 - 448x^15 + 1309x^14 + 75494x^13 - 374314x^12 - 5597667x^11 + 41830550x^10 + 136426018x^9 - 1919481097x^8 + 2548312782x^7 + 27117309376x^6 - 105628969954x^5 + 34101907629x^4 + 457076113374x^3 - 817186035962x^2 + 323264486326x + 117028501127	\( 953^{16} \)	$C_{17}$ (as 17T1)	Trivial (GRH)