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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.489639287266880371204241478228795637811.1	x^22 - 9x^21 + 48x^20 - 183x^19 + 655x^18 - 2122x^17 + 6491x^16 - 17468x^15 + 45646x^14 - 108112x^13 + 251537x^12 - 521318x^11 + 1081334x^10 - 1963079x^9 + 3653567x^8 - 5688311x^7 + 9483883x^6 - 12150619x^5 + 18112705x^4 - 17363285x^3 + 23145134x^2 - 12720749x + 15354571	\( -\,11^{11}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[15499]$ (GRH)
22.0.14844328957686912445797815584548193359375.1	x^22 - 9x^21 + 59x^20 - 273x^19 + 1195x^18 - 4387x^17 + 15557x^16 - 47572x^15 + 143444x^14 - 378050x^13 + 996721x^12 - 2278940x^11 + 5312470x^10 - 10499975x^9 + 21744445x^8 - 36444035x^7 + 67020055x^6 - 91292990x^5 + 148564990x^4 - 149610555x^3 + 214516775x^2 - 122653854x + 155003209	\( -\,3^{11}\cdot 5^{11}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[91498]$ (GRH)
22.0.4978518112499354698647829163838661251242411.1	x^22 - 11x^19 + 33x^18 + 462x^17 + 583x^16 + 1023x^15 + 5214x^14 + 8239x^13 + 31647x^12 - 7140x^11 + 18271x^10 + 320529x^9 - 276177x^8 - 359084x^7 + 861894x^6 - 236907x^5 - 210870x^4 - 339471x^3 + 277992x^2 - 96228x + 177147	\( -\,11^{41} \)	$C_{22}$ (as 22T1)	$[23651]$ (GRH)
22.0.13936571865431899047915848208912554030792704.1	x^22 + 61x^20 + 1466x^18 + 18767x^16 + 142812x^14 + 672568x^12 + 1953909x^10 + 3334358x^8 + 2944762x^6 + 969293x^4 + 57019x^2 + 841	\( -\,2^{22}\cdot 67^{20} \)	$C_{22}$ (as 22T1)	$[36961]$ (GRH)
22.0.172239967478675757728235268038638014589675547.1	x^22 - x^21 + 41x^20 + 2x^19 + 1137x^18 + 120x^17 + 15187x^16 + 4521x^15 + 143572x^14 + 41908x^13 + 810728x^12 + 310631x^11 + 3278352x^10 + 1130011x^9 + 7018057x^8 + 3087160x^7 + 10139143x^6 + 2471155x^5 + 430399x^4 + 38213x^3 + 2468x^2 + 57x + 1	\( -\,3^{11}\cdot 89^{20} \)	$C_{22}$ (as 22T1)	$[26687]$ (GRH)
22.0.174398723209634833558490883294218000698177947.1	x^22 + 20x^20 + 257x^18 - 4x^17 + 1934x^16 - 106x^15 + 10498x^14 - 1280x^13 + 38977x^12 - 9695x^11 + 107932x^10 - 38992x^9 + 209993x^8 - 108043x^7 + 304613x^6 - 168141x^5 + 295910x^4 - 171702x^3 + 186586x^2 - 69384x + 31329	\( -\,3^{11}\cdot 74843^{8} \)	22T13	$[2, 2, 2, 3580]$ (GRH)
22.0.174398723209634833558490883294218000698177947.2	x^22 - 4x^21 + 41x^20 - 62x^19 + 712x^18 - 691x^17 + 8218x^16 - 3289x^15 + 62044x^14 - 12972x^13 + 331973x^12 + 1202x^11 + 1201112x^10 + 23541x^9 + 2960817x^8 + 250587x^7 + 4248123x^6 - 781164x^5 + 3132885x^4 - 746848x^3 + 1635703x^2 - 490413x + 335241	\( -\,3^{11}\cdot 74843^{8} \)	22T13	$[2, 2, 2, 3580]$ (GRH)
22.0.15329357105602142437812938855438783298481123683.1	x^22 - x^21 + 47x^20 - 52x^19 + 792x^18 - 1785x^17 + 6826x^16 - 27519x^15 + 65725x^14 - 239894x^13 + 428795x^12 - 1132774x^11 + 3194187x^10 - 2353532x^9 + 12889600x^8 - 10825379x^7 + 17897782x^6 - 53427788x^5 + 50690086x^4 - 31652698x^3 + 43810715x^2 - 2705016x + 8609149	\( -\,3^{11}\cdot 89^{21} \)	$C_{22}$ (as 22T1)	$[51658]$ (GRH)
22.0.30154419159814893789975560365370581492704546816.1	x^22 + 66x^20 + 1815x^18 + 27225x^16 + 245025x^14 + 1367784x^12 + 4714281x^10 + 9653985x^8 + 10895445x^6 + 6145227x^4 + 1617165x^2 + 156816	\( -\,2^{12}\cdot 3^{20}\cdot 11^{32} \)	22T36	$[2, 12506]$ (GRH)
22.0.80175413461356653345578817535138847697621761947.1	x^22 + 55x^20 - 66x^19 + 2200x^18 - 2211x^17 + 36520x^16 - 15048x^15 + 407473x^14 - 67485x^13 + 2823634x^12 + 317505x^11 + 14038057x^10 + 2608749x^9 + 46593316x^8 + 11785983x^7 + 109177024x^6 + 15287250x^5 + 140760675x^4 + 3952476x^3 + 120982653x^2 - 2670327x + 59049	\( -\,3^{11}\cdot 11^{40} \)	$C_{22}$ (as 22T1)	$[2, 2, 2, 2, 2, 2, 2, 2, 2, 178]$ (GRH)
22.0.1898310766666226673632489495745922930975549947904.1	x^22 + 110x^20 + 4675x^18 + 101783x^16 + 1279201x^14 + 9871136x^12 + 48063862x^10 + 147421505x^8 + 274663048x^6 + 281918538x^4 + 121207185x^2 + 59049	\( -\,2^{22}\cdot 11^{40} \)	$C_{22}$ (as 22T1)	$[14411]$ (GRH)
22.0.243091704711882553644913533390559631408320849609375.1	x^22 + 110x^20 - 22x^19 + 4895x^18 + 4026x^17 + 120120x^16 + 288222x^15 + 1882144x^14 + 6515520x^13 + 24762320x^12 + 60773360x^11 + 227012456x^10 + 397249116x^9 + 720148935x^8 + 1566072057x^7 + 1566926449x^6 + 1217292384x^5 + 714471362x^4 - 2592915589x^3 + 2027899907x^2 - 2522739483x + 6490917711	\( -\,5^{11}\cdot 11^{41} \)	$C_{22}$ (as 22T1)	$[88708]$ (GRH)