Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Results (28 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
11.11.41426511213649.1	x^11 - x^10 - 10x^9 + 9x^8 + 36x^7 - 28x^6 - 56x^5 + 35x^4 + 35x^3 - 15x^2 - 6x + 1	$11$	[11,0]	$23^{10}$	$1$	$17.2955507649$		✓	✓	$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1014.31330506$
11.11.182...449.1	x^11 - x^10 - 30x^9 + 63x^8 + 220x^7 - 698x^6 - 101x^5 + 1960x^4 - 1758x^3 + 35x^2 + 243x + 29	$11$	[11,0]	$67^{10}$	$1$	$45.7159766745$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$330512.248088$
11.11.311...601.1	x^11 - x^10 - 40x^9 + 19x^8 + 482x^7 - 84x^6 - 2185x^5 - 102x^4 + 3152x^3 + 781x^2 + 57x + 1	$11$	[11,0]	$89^{10}$	$1$	$59.1796964646$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$846366.485722$
11.11.672...201.1	x^11 - 55x^9 - 33x^8 + 825x^7 + 396x^6 - 4972x^5 - 1287x^4 + 12760x^3 + 924x^2 - 10989x - 243	$11$	[11,0]	$11^{20}$	$1$	$78.2422346586$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$278432564.723$
11.11.973...001.1	x^11 - x^10 - 90x^9 + 115x^8 + 2349x^7 - 943x^6 - 26327x^5 - 21284x^4 + 102168x^3 + 217794x^2 + 148930x + 30647	$11$	[11,0]	$199^{10}$	$1$	$122.989046087$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$114390451.519$
11.11.157...801.1	x^11 - x^10 - 150x^9 + 402x^8 + 6577x^7 - 28617x^6 - 62124x^5 + 475464x^4 - 343344x^3 - 1913488x^2 + 4015168x - 2287616	$11$	[11,0]	$331^{10}$	$1$	$195.322701164$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1340143683620$
11.11.300...049.1	x^11 - x^10 - 160x^9 + 525x^8 + 6066x^7 - 26034x^6 - 48369x^5 + 265374x^4 - 42966x^3 - 405001x^2 + 63189x + 170569	$11$	[11,0]	$353^{10}$	$1$	$207.08985455$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$5373530988.23$
11.11.972...049.1	x^11 - x^10 - 180x^9 + 13x^8 + 11655x^7 + 12159x^6 - 316973x^5 - 720142x^4 + 2670510x^3 + 10551746x^2 + 10752776x + 3098903	$11$	[11,0]	$397^{10}$	$1$	$230.428835104$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1592800927.62$
11.11.166...801.1	x^11 - x^10 - 190x^9 + 547x^8 + 10985x^7 - 51221x^6 - 141765x^5 + 1224028x^4 - 2399676x^3 + 1263744x^2 + 873500x - 785489	$11$	[11,0]	$419^{10}$	$1$	$242.008672808$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$13726169613.8$
11.11.452...849.1	x^11 - x^10 - 210x^9 + 857x^8 + 6242x^7 - 36336x^6 - 8398x^5 + 289307x^4 - 265801x^3 - 519569x^2 + 455080x + 344327	$11$	[11,0]	$463^{10}$	$1$	$265.005841026$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$5780480495.29$
11.11.799...449.1	x^11 - x^10 - 280x^9 + 469x^8 + 14891x^7 - 24713x^6 - 271477x^5 + 355512x^4 + 1733428x^3 - 1151536x^2 - 2438066x + 391619	$11$	[11,0]	$617^{10}$	$1$	$344.051041126$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$11014089072.5$
11.11.159...601.1	x^11 - x^10 - 300x^9 + 2185x^8 + 8376x^7 - 135886x^6 + 437196x^5 + 166743x^4 - 4024987x^3 + 9615051x^2 - 9696452x + 3691321	$11$	[11,0]	$661^{10}$	$1$	$366.285316023$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$17494437669.3$
11.11.220...449.1	x^11 - x^10 - 310x^9 + 395x^8 + 26441x^7 - 57583x^6 - 744575x^5 + 2220564x^4 + 2568726x^3 - 5088204x^2 - 1360638x + 996543	$11$	[11,0]	$683^{10}$	$1$	$377.351511793$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$2276941413140$
11.11.412...649.1	x^11 - x^10 - 330x^9 - 637x^8 + 30782x^7 + 122078x^6 - 616689x^5 - 3355168x^4 + 183306x^3 + 17584739x^2 + 19842261x + 2279191	$11$	[11,0]	$727^{10}$	$1$	$399.387914504$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$49130453388.1$
11.11.218...401.1	x^11 - x^10 - 390x^9 + 653x^8 + 52046x^7 - 146438x^6 - 2723930x^5 + 11558015x^4 + 36326009x^3 - 250960565x^2 + 385923388x - 145865807	$11$	[11,0]	$859^{10}$	$1$	$464.80042081$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$80664010957.6$
11.11.281...801.1	x^11 - x^10 - 400x^9 + 29x^8 + 34594x^7 - 51208x^6 - 648406x^5 + 1281923x^4 + 1931229x^3 - 2774565x^2 - 1474244x + 1306999	$11$	[11,0]	$881^{10}$	$1$	$475.609834056$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$379023342573$
11.11.580...049.1	x^11 - x^10 - 430x^9 - 2035x^8 + 28780x^7 + 141142x^6 - 760875x^5 - 3028650x^4 + 8674010x^3 + 20981317x^2 - 30077229x - 47440673	$11$	[11,0]	$947^{10}$	$1$	$507.893562454$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1104123814020$
11.11.913...401.1	x^11 - x^10 - 450x^9 + 393x^8 + 65785x^7 - 76121x^6 - 3728249x^5 + 6483322x^4 + 89323866x^3 - 205338716x^2 - 745717454x + 2032282741	$11$	[11,0]	$991^{10}$	$1$	$529.301740716$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$155801246971$
11.11.278...449.1	x^11 - 1265x^9 - 4807x^8 + 544962x^7 + 4031808x^6 - 81455880x^5 - 916234187x^4 + 714773070x^3 + 31567681332x^2 + 58422539890x - 98108643071	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$2524169127627.655$
11.11.278...449.2	x^11 - 1265x^9 - 4807x^8 + 528264x^7 + 3347190x^6 - 77350955x^5 - 506615549x^4 + 4435947417x^3 + 22379726501x^2 - 83401753347x - 84992124733	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$13856724912536.113$
11.11.278...449.3	x^11 - 1265x^9 - 759x^8 + 461472x^7 + 727122x^6 - 64557504x^5 - 152866395x^4 + 3259832136x^3 + 7537075436x^2 - 51546842380x - 79493912081	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$2768761764338.989$
11.11.278...449.4	x^11 - 1265x^9 - 4807x^8 + 478170x^7 + 3280398x^6 - 48772328x^5 - 446246713x^4 + 942027284x^3 + 16580057472x^2 + 32566872448x - 22424006285	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$50372046418790.55$
11.11.278...449.5	x^11 - 1265x^9 - 14674x^8 + 185955x^7 + 2435884x^6 - 11416119x^5 - 129158018x^4 + 313069284x^3 + 2487077032x^2 - 2608377376x - 15433395968	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$5237308266600679.0$
11.11.278...449.6	x^11 - 1265x^9 - 759x^8 + 511566x^7 + 810612x^6 - 74117109x^5 - 171278723x^4 + 3526980655x^3 + 9233082947x^2 - 12188156343x - 5403811843	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$3514735062507.8184$
11.11.278...449.7	x^11 - 1265x^9 - 759x^8 + 344586x^7 - 436172x^6 - 27487944x^5 + 90501389x^4 + 123836416x^3 - 487081672x^2 + 106500350x + 236115769	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$2963701738171.1094$
11.11.278...449.8	x^11 - 1265x^9 - 10373x^8 + 294492x^7 + 3035494x^6 - 8026425x^5 - 146495349x^4 - 384865371x^3 - 62619271x^2 + 570245555x + 370255403	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$22723991241313.113$
11.11.278...449.9	x^11 - 1265x^9 - 17457x^8 + 94116x^7 + 2769844x^6 + 11844195x^5 - 25677729x^4 - 204142917x^3 - 41615211x^2 + 796965433x + 479405629	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$2107938978012.7551$
11.11.278...449.10	x^11 - 1265x^9 - 10373x^8 + 461472x^7 + 7026316x^6 - 19353235x^5 - 853505367x^4 - 3771314393x^3 + 11665833289x^2 + 103006408615x + 152668956353	$11$	[11,0]	$11^{20}\cdot 23^{10}$	$2$	$1353.2425415$		✓		$C_{11}$ (as 11T1)	$[11]$	$2$	$10$	$2083946923676.7688$