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 25 matches)

Label	Polynomial	Discriminant	Galois group	Class group
11.1.67274999493256000920100000000000.1	x^11 - 55x^9 - 330x^8 - 990x^7 - 1848x^6 - 2310x^5 - 1980x^4 - 1155x^3 - 440x^2 - 99x + 109999999990	\( -\,2^{11}\cdot 5^{11}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.1.127083146233027522514188173344768.1	x^11 - 154x^9 - 308x^8 + 9009x^7 + 35420x^6 - 259952x^5 - 2978272x^4 - 16783536x^3 - 65231936x^2 - 147702016x - 142879744	\( -\,2^{15}\cdot 7^{8}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.3.166619625871733889625740432900096.1	x^11 - 154x^9 - 308x^8 + 9009x^7 + 35420x^6 - 217360x^5 - 1721808x^4 - 3611960x^3 - 534688x^2 + 4777344x + 1034752	\( 2^{22}\cdot 3^{10}\cdot 11^{20} \)	$A_{11}$ (as 11T7)	$[11]$ (GRH)
11.1.1201015904309083794984173196083712.1	x^11 - 99x^9 - 462x^8 + 1584x^7 + 22176x^6 + 96096x^5 + 234432x^4 + 354816x^3 + 332288x^2 + 177408x + 15630408	\( -\,2^{9}\cdot 3^{20}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.1.1603055691937203834185244205775343.1	x^11 - 11x^9 - 77x^8 + 396x^7 + 8316x^6 + 54054x^5 + 197802x^4 + 449064x^3 + 630828x^2 + 505197x + 177147	\( -\,3^{10}\cdot 7^{9}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.3.1710040223127582200280199726455129.1	x^11 - 39135393x^2 + 1056655611	\( 3^{26}\cdot 11^{20} \)	$A_{11}$ (as 11T7)	$[11]$ (GRH)
11.3.26279296677053125359414062500000000.1	x^11 - 55x^9 - 330x^8 - 990x^7 - 1848x^6 - 2310x^5 - 1980x^4 - 1155x^3 - 440x^2 - 99x + 3519999990	\( 2^{8}\cdot 5^{16}\cdot 11^{20} \)	$A_{11}$ (as 11T7)	$[11]$ (GRH)
11.3.27555839792437657976872960000000000.1	x^11 + 110x^9 - 2860x^8 + 91025x^7 - 133980x^6 - 6042410x^5 + 114912820x^4 - 552727725x^3 + 5702365240x^2 - 34495524800x + 59609831680	\( 2^{22}\cdot 5^{10}\cdot 11^{20} \)	$A_{11}$ (as 11T7)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.1	x^11 - 1265x^9 - 4807x^8 + 544962x^7 + 4031808x^6 - 81455880x^5 - 916234187x^4 + 714773070x^3 + 31567681332x^2 + 58422539890x - 98108643071	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.2	x^11 - 1265x^9 - 4807x^8 + 528264x^7 + 3347190x^6 - 77350955x^5 - 506615549x^4 + 4435947417x^3 + 22379726501x^2 - 83401753347x - 84992124733	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.3	x^11 - 1265x^9 - 759x^8 + 461472x^7 + 727122x^6 - 64557504x^5 - 152866395x^4 + 3259832136x^3 + 7537075436x^2 - 51546842380x - 79493912081	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.4	x^11 - 1265x^9 - 4807x^8 + 478170x^7 + 3280398x^6 - 48772328x^5 - 446246713x^4 + 942027284x^3 + 16580057472x^2 + 32566872448x - 22424006285	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.5	x^11 - 1265x^9 - 14674x^8 + 185955x^7 + 2435884x^6 - 11416119x^5 - 129158018x^4 + 313069284x^3 + 2487077032x^2 - 2608377376x - 15433395968	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.6	x^11 - 1265x^9 - 759x^8 + 511566x^7 + 810612x^6 - 74117109x^5 - 171278723x^4 + 3526980655x^3 + 9233082947x^2 - 12188156343x - 5403811843	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.7	x^11 - 1265x^9 - 759x^8 + 344586x^7 - 436172x^6 - 27487944x^5 + 90501389x^4 + 123836416x^3 - 487081672x^2 + 106500350x + 236115769	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.8	x^11 - 1265x^9 - 10373x^8 + 294492x^7 + 3035494x^6 - 8026425x^5 - 146495349x^4 - 384865371x^3 - 62619271x^2 + 570245555x + 370255403	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.9	x^11 - 1265x^9 - 17457x^8 + 94116x^7 + 2769844x^6 + 11844195x^5 - 25677729x^4 - 204142917x^3 - 41615211x^2 + 796965433x + 479405629	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.11.27869685209056005146671841116784449.10	x^11 - 1265x^9 - 10373x^8 + 461472x^7 + 7026316x^6 - 19353235x^5 - 853505367x^4 - 3771314393x^3 + 11665833289x^2 + 103006408615x + 152668956353	\( 11^{20}\cdot 23^{10} \)	$C_{11}$ (as 11T1)	$[11]$ (GRH)
11.3.31423265337037027486797829775390625.1	x^11 - 3025x^8 - 18150x^7 + 390225x^6 - 2498650x^5 + 105215550x^4 - 916892625x^3 + 404956750x^2 + 8463163500x + 9205180875	\( 3^{14}\cdot 5^{10}\cdot 11^{20} \)	$A_{11}$ (as 11T7)	$[11]$ (GRH)
11.1.41040965355061972806724793434923096.1	x^11 - 13045131x^2 - 704437074	\( -\,2^{3}\cdot 3^{27}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.1.113745664595103668651172135526465536.1	x^11 + 1936x^7 + 937024x^3 - 261685248	\( -\,2^{33}\cdot 3^{9}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[22]$ (GRH)
11.1.266985804842311696361995078675689472.1	x^11 + 484x^7 - 8348032	\( -\,2^{12}\cdot 7^{13}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.1.341236993785311005953516406579396608.3	x^11 - 2178x^8 - 43717791744	\( -\,2^{33}\cdot 3^{10}\cdot 11^{20} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)
11.3.946405652456836696490269155592519936.2	x^11 + 10x^9 - 401x^8 + 66x^7 - 2175x^6 + 48090x^5 + 10109x^4 - 50807x^3 - 29097x^2 - 3376x - 4	\( 2^{8}\cdot 41^{8}\cdot 47^{4}\cdot 3121^{4} \)	$\PSL(2,11)$ (as 11T5)	$[12]$ (GRH)
11.1.796667468142213432406523937904342448734208.1	x^11 - 7784239034x^3 - 17810338909792	\( -\,2^{33}\cdot 11^{20}\cdot 13^{10} \)	$S_{11}$ (as 11T8)	$[11]$ (GRH)