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 matches 1-50 of 54)

Label	Polynomial	Discriminant	Galois group	Class group
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	\( 23^{10} \)	$C_{11}$ (as 11T1)	Trivial
11.11.48706494267293.1	x^11 - 3x^10 - 8x^9 + 28x^8 + 15x^7 - 87x^6 + 16x^5 + 95x^4 - 51x^3 - 17x^2 + 13x - 1	\( 421\cdot 115692385433 \)	$S_{11}$ (as 11T8)	Trivial
11.11.55029067682009.1	x^11 - x^10 - 11x^9 + 9x^8 + 41x^7 - 24x^6 - 60x^5 + 16x^4 + 34x^3 + 2x^2 - 5x - 1	\( 55029067682009 \)	$S_{11}$ (as 11T8)	Trivial
11.11.57451466331409.1	x^11 - 12x^9 - 5x^8 + 46x^7 + 32x^6 - 57x^5 - 43x^4 + 23x^3 + 16x^2 - x - 1	\( 233\cdot 246572816873 \)	$S_{11}$ (as 11T8)	Trivial
11.11.89814305807257.1	x^11 - x^10 - 12x^9 + 10x^8 + 53x^7 - 35x^6 - 108x^5 + 51x^4 + 102x^3 - 27x^2 - 36x + 1	\( 2053\cdot 43747835269 \)	$S_{11}$ (as 11T8)	Trivial
11.11.96470357797337.1	x^11 - 2x^10 - 10x^9 + 15x^8 + 38x^7 - 36x^6 - 61x^5 + 36x^4 + 38x^3 - 15x^2 - 6x + 1	\( 137\cdot 293\cdot 11093\cdot 216649 \)	$S_{11}$ (as 11T8)	Trivial
11.11.104215884017569.1	x^11 - 3x^10 - 8x^9 + 26x^8 + 15x^7 - 60x^6 - 11x^5 + 49x^4 + 4x^3 - 14x^2 - x + 1	\( 1451\cdot 71823490019 \)	$S_{11}$ (as 11T8)	Trivial
11.11.129171716734329.1	x^11 - 2x^10 - 10x^9 + 21x^8 + 32x^7 - 72x^6 - 40x^5 + 100x^4 + 17x^3 - 51x^2 + 3	\( 3^{3}\cdot 4784137656827 \)	$S_{11}$ (as 11T8)	Trivial
11.11.167643906155581.1	x^11 - x^10 - 13x^9 + 19x^8 + 42x^7 - 73x^6 - 40x^5 + 88x^4 + 8x^3 - 34x^2 + 3x + 1	\( 233\cdot 937\cdot 5279\cdot 145459 \)	$S_{11}$ (as 11T8)	Trivial
11.11.176300559557501.1	x^11 - 13x^9 - 7x^8 + 53x^7 + 53x^6 - 55x^5 - 86x^4 - 18x^3 + 16x^2 + 8x + 1	\( 7786721\cdot 22641181 \)	$S_{11}$ (as 11T8)	Trivial
11.11.3670285774226257.1	x^11 - 5x^10 - 4x^9 + 54x^8 - 53x^7 - 127x^6 + 208x^5 + 69x^4 - 222x^3 + 29x^2 + 56x - 5	\( 1297^{5} \)	$D_{11}$ (as 11T2)	Trivial
11.11.1035571956771279049.1	x^11 - 5x^10 - 18x^9 + 114x^8 + 37x^7 - 856x^6 + 746x^5 + 2117x^4 - 3648x^3 + 135x^2 + 2677x - 1301	\( 19^{5}\cdot 211^{5} \)	$D_{11}$ (as 11T2)	Trivial
11.11.1822837804551761449.1	x^11 - x^10 - 30x^9 + 63x^8 + 220x^7 - 698x^6 - 101x^5 + 1960x^4 - 1758x^3 + 35x^2 + 243x + 29	\( 67^{10} \)	$C_{11}$ (as 11T1)	Trivial
11.11.3483293138903825541.1	x^11 - 4x^10 - 17x^9 + 78x^8 + 75x^7 - 494x^6 - 8x^5 + 1260x^4 - 522x^3 - 1122x^2 + 748x - 9	\( 3^{5}\cdot 7^{5}\cdot 31^{8} \)	$F_{11}$ (as 11T4)	Trivial
11.11.4910318845910094848.1	x^11 - 22x^9 + 176x^7 - 616x^5 + 880x^3 - 352x - 88	\( 2^{10}\cdot 7^{5}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.11.8315244373648414401.1	x^11 - 2x^10 - 32x^9 + 86x^8 + 284x^7 - 1057x^6 - 293x^5 + 4084x^4 - 3446x^3 - 2439x^2 + 4158x - 1323	\( 3^{5}\cdot 2027^{5} \)	$D_{11}$ (as 11T2)	Trivial
11.11.31181719929966183601.1	x^11 - x^10 - 40x^9 + 19x^8 + 482x^7 - 84x^6 - 2185x^5 - 102x^4 + 3152x^3 + 781x^2 + 57x + 1	\( 89^{10} \)	$C_{11}$ (as 11T1)	Trivial
11.11.31376518243389673201.1	x^11 - 4x^10 - 25x^9 + 81x^8 + 237x^7 - 562x^6 - 1010x^5 + 1574x^4 + 1805x^3 - 1586x^2 - 847x + 579	\( 74843^{4} \)	$\PSL(2,11)$ (as 11T5)	Trivial
11.11.31376518243389673201.2	x^11 - 20x^9 + 143x^7 - 4x^6 - 463x^5 + 54x^4 + 691x^3 - 186x^2 - 392x + 177	\( 74843^{4} \)	$\PSL(2,11)$ (as 11T5)	Trivial
11.11.123610132462587890625.1	x^11 - x^10 - 20x^9 + 30x^8 + 105x^7 - 207x^6 - 63x^5 + 240x^4 - 15x^3 - 80x^2 + 11x + 4	\( 3^{10}\cdot 5^{10}\cdot 11^{8} \)	$C_{11}:C_5$ (as 11T3)	Trivial
11.11.552054582080600113152.1	x^11 - 33x^9 + 396x^7 - 2079x^5 + 4455x^3 - 2673x - 810	\( 2^{15}\cdot 3^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.11.672749994932560009201.1	x^11 - 55x^9 - 33x^8 + 825x^7 + 396x^6 - 4972x^5 - 1287x^4 + 12760x^3 + 924x^2 - 10989x - 243	\( 11^{20} \)	$C_{11}$ (as 11T1)	Trivial
11.11.2713285598714072534889.1	x^11 - 33x^9 + 396x^7 - 2079x^5 + 4455x^3 - 2673x - 837	\( 3^{10}\cdot 11^{16} \)	$C_{11}:C_5$ (as 11T3)	Trivial
11.11.2853116706110000000000.1	x^11 - 55x^9 + 1100x^7 - 9625x^5 + 34375x^3 - 34375x - 13900	\( 2^{10}\cdot 5^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.97393677359695041798001.1	x^11 - x^10 - 90x^9 + 115x^8 + 2349x^7 - 943x^6 - 26327x^5 - 21284x^4 + 102168x^3 + 217794x^2 + 148930x + 30647	\( 199^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.193763450514676380800000.1	x^11 - x^10 - 53x^9 + 31x^8 + 996x^7 - 28x^6 - 7812x^5 - 5784x^4 + 20673x^3 + 36219x^2 + 19909x + 3279	\( 2^{10}\cdot 5^{5}\cdot 7^{10}\cdot 11^{8} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.448727830698946884765625.1	x^11 - 55x^9 + 1100x^7 - 9625x^5 + 34375x^3 - 34375x - 12675	\( 5^{10}\cdot 11^{16} \)	$C_{11}:C_5$ (as 11T3)	Trivial (GRH)
11.11.15786284949774657045043801.1	x^11 - x^10 - 150x^9 + 402x^8 + 6577x^7 - 28617x^6 - 62124x^5 + 475464x^4 - 343344x^3 - 1913488x^2 + 4015168x - 2287616	\( 331^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.30043259834681392663962049.1	x^11 - x^10 - 160x^9 + 525x^8 + 6066x^7 - 26034x^6 - 48369x^5 + 265374x^4 - 42966x^3 - 405001x^2 + 63189x + 170569	\( 353^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.97253461433805715000527049.1	x^11 - x^10 - 180x^9 + 13x^8 + 11655x^7 + 12159x^6 - 316973x^5 - 720142x^4 + 2670510x^3 + 10551746x^2 + 10752776x + 3098903	\( 397^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.166778563814477267272573801.1	x^11 - x^10 - 190x^9 + 547x^8 + 10985x^7 - 51221x^6 - 141765x^5 + 1224028x^4 - 2399676x^3 + 1263744x^2 + 873500x - 785489	\( 419^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.452699390921229872008282849.1	x^11 - x^10 - 210x^9 + 857x^8 + 6242x^7 - 36336x^6 - 8398x^5 + 289307x^4 - 265801x^3 - 519569x^2 + 455080x + 344327	\( 463^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.7995610696842977761957082449.1	x^11 - x^10 - 280x^9 + 469x^8 + 14891x^7 - 24713x^6 - 271477x^5 + 355512x^4 + 1733428x^3 - 1151536x^2 - 2438066x + 391619	\( 617^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.15922622355555940184939928601.1	x^11 - x^10 - 300x^9 + 2185x^8 + 8376x^7 - 135886x^6 + 437196x^5 + 166743x^4 - 4024987x^3 + 9615051x^2 - 9696452x + 3691321	\( 661^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.22090575837180674640752471449.1	x^11 - x^10 - 310x^9 + 395x^8 + 26441x^7 - 57583x^6 - 744575x^5 + 2220564x^4 + 2568726x^3 - 5088204x^2 - 1360638x + 996543	\( 683^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.41242416955341131537413053649.1	x^11 - x^10 - 330x^9 - 637x^8 + 30782x^7 + 122078x^6 - 616689x^5 - 3355168x^4 + 183306x^3 + 17584739x^2 + 19842261x + 2279191	\( 727^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.218741727855135890482344953401.1	x^11 - x^10 - 390x^9 + 653x^8 + 52046x^7 - 146438x^6 - 2723930x^5 + 11558015x^4 + 36326009x^3 - 250960565x^2 + 385923388x - 145865807	\( 859^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.281681992520036568627910696801.1	x^11 - x^10 - 400x^9 + 29x^8 + 34594x^7 - 51208x^6 - 648406x^5 + 1281923x^4 + 1931229x^3 - 2774565x^2 - 1474244x + 1306999	\( 881^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.580095892065127629623589183049.1	x^11 - x^10 - 430x^9 - 2035x^8 + 28780x^7 + 141142x^6 - 760875x^5 - 3028650x^4 + 8674010x^3 + 20981317x^2 - 30077229x - 47440673	\( 947^{10} \)	$C_{11}$ (as 11T1)	Trivial (GRH)
11.11.913558883040682586951726894401.1	x^11 - x^10 - 450x^9 + 393x^8 + 65785x^7 - 76121x^6 - 3728249x^5 + 6483322x^4 + 89323866x^3 - 205338716x^2 - 745717454x + 2032282741	\( 991^{10} \)	$C_{11}$ (as 11T1)	Trivial (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)