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Results (1-50 of 57 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
7.1.128252814507.1	$x^{7} - 3 x^{6} - 2 x^{5} + 60 x^{4} - 14 x^{3} + 102 x^{2} + 3 x + 45$	$7$	[1,3]	$-\,3^{3}\cdot 41^{6}$	$2$	$38.624840643$	$41.77791772275626$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$8015.31677379$
7.1.128252814507.2	$x^{7} - x^{6} - 23 x^{5} + 66 x^{4} - 27 x^{3} - 34 x^{2} - 55 x + 94$	$7$	[1,3]	$-\,3^{3}\cdot 41^{6}$	$2$	$38.624840643$	$86.90157081589874$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1610.90281962$
7.1.1629285754663.1	$x^{7} - 82 x^{4} - 41 x^{3} + 656 x^{2} - 82 x + 123$	$7$	[1,3]	$-\,7^{3}\cdot 41^{6}$	$2$	$55.5355448729$	$63.816823447389226$			?	$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$6502.15269071$
7.1.6322388744771.1	$x^{7} - 2 x^{6} - 10 x^{5} - 46 x^{4} - 22 x^{3} - 22 x^{2} + 129 x - 104$	$7$	[1,3]	$-\,11^{3}\cdot 41^{6}$	$2$	$67.405807176$	$79.99862186676157$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$17351.2097466$
7.1.16031601813375.1	$x^{7} - 2 x^{6} - 10 x^{5} + 77 x^{4} - 63 x^{3} - 555 x^{2} + 1728 x - 1539$	$7$	[1,3]	$-\,3^{3}\cdot 5^{3}\cdot 41^{6}$	$3$	$76.9883964305$	$93.4182639864762$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$60504.7616367$
7.1.18468405289008.1	$x^{7} - 3 x^{6} - 2 x^{5} - 22 x^{4} + 109 x^{3} - 103 x^{2} + 1356 x - 4096$	$7$	[1,3]	$-\,2^{4}\cdot 3^{5}\cdot 41^{6}$	$3$	$78.5604928812$	$112.88059467209163$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$122361.057384$
7.1.18468405289008.2	$x^{7} - 3 x^{6} - 2 x^{5} - 22 x^{4} + 109 x^{3} - 103 x^{2} + 372 x - 160$	$7$	[1,3]	$-\,2^{4}\cdot 3^{5}\cdot 41^{6}$	$3$	$78.5604928812$	$145.5448871691979$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$137617.347413$
7.1.25289554979084.1	$x^{7} - x^{6} + 18 x^{5} + 25 x^{4} + 96 x^{3} + 376 x^{2} + 560 x + 176$	$7$	[1,3]	$-\,2^{2}\cdot 11^{3}\cdot 41^{6}$	$3$	$82.1685993203$	$231.26895634875254$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$28667.7977519$
7.1.32580964989019.1	$x^{7} - 2 x^{6} + 31 x^{5} + 118 x^{4} + 265 x^{3} + 3340 x^{2} + 4024 x + 21544$	$7$	[1,3]	$-\,19^{3}\cdot 41^{6}$	$2$	$85.1968269783$	$105.13878728572445$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$54001.637289$
7.1.32832720513792.1	$x^{7} - 123 x^{3} + 164 x - 984$	$7$	[1,3]	$-\,2^{8}\cdot 3^{3}\cdot 41^{6}$	$3$	$85.2905630425$	$347.60628326359495$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$39936.8128717$
7.1.41553911900268.1	$x^{7} - 3 x^{6} - 2 x^{5} - 22 x^{4} - 14 x^{3} + 20 x^{2} + 3 x - 37$	$7$	[1,3]	$-\,2^{2}\cdot 3^{7}\cdot 41^{6}$	$3$	$88.2096274412$	$286.9426646487621$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$73838.7145413$
7.1.65665441027584.1	$x^{7} - 3 x^{6} - 2 x^{5} + 142 x^{4} - 1367 x^{3} + 3013 x^{2} - 6024 x + 51664$	$7$	[1,3]	$-\,2^{9}\cdot 3^{3}\cdot 41^{6}$	$3$	$94.1684162705$	$118.16579570245838$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$575233.393911$
7.1.79835001978487.1	$x^{7} - 2 x^{6} + 31 x^{5} - 169 x^{4} + 19 x^{3} - 1908 x^{2} + 293 x - 473$	$7$	[1,3]	$-\,7^{5}\cdot 41^{6}$	$2$	$96.8339438298$	$122.077191557991$			?	$F_7$ (as 7T4)	trivial	trivial	$2$	$3$	$60302.6606967$
7.1.203660719332875.1	$x^{7} - 3 x^{6} - 2 x^{5} - 22 x^{4} + 232 x^{3} - 1046 x^{2} + 2709 x - 2989$	$7$	[1,3]	$-\,5^{3}\cdot 7^{3}\cdot 41^{6}$	$3$	$110.695409314$	$142.69875533646479$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$217463.014797$
7.1.295494484624128.1	$x^{7} - 3 x^{6} - 2 x^{5} - 22 x^{4} + 109 x^{3} - 103 x^{2} - 120 x - 652$	$7$	[1,3]	$-\,2^{8}\cdot 3^{5}\cdot 41^{6}$	$3$	$116.740443773$	$347.60628326359495$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$866156.089444$
7.1.332431295202144.1	$x^{7} - 3 x^{6} + 39 x^{5} - 63 x^{4} + 27 x^{3} - 513 x^{2} - 243 x - 3645$	$7$	[1,3]	$-\,2^{5}\cdot 3^{7}\cdot 41^{6}$	$3$	$118.721354565$	$644.164502217998$			?	$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$3$	$271407.927349$
7.1.493170072613343.1	$x^{7} - 2 x^{6} + 31 x^{5} - 87 x^{4} - 719 x^{3} - 7074 x^{2} - 10408 x - 15151$	$7$	[1,3]	$-\,41^{6}\cdot 47^{3}$	$2$	$125.602860611$	$165.3617622413773$			?	$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$28029.9080703$
7.1.667902657118528.1	$x^{7} - 3 x^{6} + 39 x^{5} + 19 x^{4} + 1339 x^{3} - 4449 x^{2} + 26325 x + 23497$	$7$	[1,3]	$-\,2^{6}\cdot 13^{3}\cdot 41^{6}$	$3$	$131.164457495$	$173.93534170391055$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$1106479.50463$
7.1.790298593096375.1	$x^{7} - 328 x^{4} - 1148 x^{3} - 7954 x^{2} - 13243 x - 44403$	$7$	[1,3]	$-\,5^{3}\cdot 11^{3}\cdot 41^{6}$	$3$	$134.355635342$	$178.88235660038$			?	$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$167420.117415$
7.1.834194306387456.1	$x^{7} - 2 x^{6} - 10 x^{5} + 200 x^{4} - 801 x^{3} + 1946 x^{2} - 2618 x + 1372$	$7$	[1,3]	$-\,2^{9}\cdot 7^{3}\cdot 41^{6}$	$3$	$135.397174987$	$180.50123445373436$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$723874.06523$
7.1.1329725180808576.1	$x^{7} - 3 x^{6} + 39 x^{5} - 145 x^{4} + 519 x^{3} - 1989 x^{2} + 3201 x - 1431$	$7$	[1,3]	$-\,2^{7}\cdot 3^{7}\cdot 41^{6}$	$3$	$144.72295226$	$718.3343720117198$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1481588.34236$
7.1.1428655601835883.1	$x^{7} - 3 x^{6} - 43 x^{5} + 101 x^{4} + 1339 x^{3} + 3095 x^{2} + 4062 x + 5580$	$7$	[1,3]	$-\,41^{6}\cdot 67^{3}$	$2$	$146.214232786$	$197.4347364064973$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$517037.637146$
7.1.1493584776706112.1	$x^{7} - 410 x^{4} - 3239 x^{3} - 14514 x^{2} - 30750 x - 32800$	$7$	[1,3]	$-\,2^{6}\cdot 17^{3}\cdot 41^{6}$	$3$	$147.145547582$	$198.90267287374382$				$D_{7}$ (as 7T2)	trivial	trivial	$2$	$3$	$855622.527269$
7.1.3911915096945863.1	$x^{7} - 41$	$7$	[1,3]	$-\,7^{7}\cdot 41^{6}$	$2$	$168.843444304$	$212.85855639452325$			✓	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$56495.4261334$
7.1.5109440126623168.1	$x^{7} - 656$	$7$	[1,3]	$-\,2^{6}\cdot 7^{5}\cdot 41^{6}$	$3$	$175.409588861$	$221.13640252190092$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$48564.1839114$
7.1.15647660387783452.1	$x^{7} + 287 x^{3} - 1722 x^{2} + 4592 x - 8774$	$7$	[1,3]	$-\,2^{2}\cdot 7^{7}\cdot 41^{6}$	$3$	$205.822464029$	$337.8918963410985$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$472359.533009$
7.1.191683839750347287.1	$x^{7} - 574 x^{4} + 1722 x^{3} + 5166 x^{2} - 28987 x + 98769$	$7$	[1,3]	$-\,7^{9}\cdot 41^{6}$	$2$	$294.402020169$	$338.30228526020807$			?	$D_{7}$ (as 7T2)	$[2, 2, 14]$	$[2, 2, 14]$	$2$	$3$	$41371.6564071$
7.1.191683839750347287.2	$x^{7} - 574 x^{4} + 2870 x^{3} - 9758 x^{2} + 23247 x + 96309$	$7$	[1,3]	$-\,7^{9}\cdot 41^{6}$	$2$	$294.4020201688223$	$338.30228526020807$			?	$D_{7}$ (as 7T2)	$[2, 2, 14]$	$[2, 2, 14]$	$2$	$3$	$29947.64600430874$
7.1.250362566204535232.1	$x^{7} - 287 x^{3} - 1148 x^{2} + 574 x - 4756$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$602.0549146405862$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$11947988.3513$
7.1.250362566204535232.2	$x^{7} - 2624$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$385.5820633351461$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$314505.884504$
7.1.250362566204535232.3	$x^{7} + 287 x^{3} + 1148 x - 2624$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$602.0549146405862$			?	$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$3$	$2052293.12106$
7.1.250362566204535232.4	$x^{7} - 1312$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$385.5820633351461$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$292004.720228$
7.1.250362566204535232.5	$x^{7} - 328$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$385.5820633351461$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$261426.705201$
7.1.250362566204535232.6	$x^{7} - 164$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$385.5820633351461$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$288048.240465$
7.1.250362566204535232.7	$x^{7} - 82$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$305.851006124$	$385.5820633351461$			✓	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$262625.391662$
7.1.2851786105673534127.1	$x^{7} - 3321$	$7$	[1,3]	$-\,3^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$432.957511152$	$545.8234471813028$			?	$F_7$ (as 7T4)	$[7, 7]$	$[7, 7]$	$2$	$3$	$188659.053569$
7.1.2851786105673534127.2	$x^{7} - 1107$	$7$	[1,3]	$-\,3^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$432.957511152$	$545.8234471813028$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$1251009.94771$
7.1.2851786105673534127.3	$x^{7} - 369$	$7$	[1,3]	$-\,3^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$432.957511152$	$545.8234471813028$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$1261187.83374$
7.1.2851786105673534127.4	$x^{7} - 123$	$7$	[1,3]	$-\,3^{6}\cdot 7^{7}\cdot 41^{6}$	$3$	$432.957511152$	$545.8234471813028$			✓	$F_7$ (as 7T4)	$[14]$	$[14]$	$2$	$3$	$658402.154528$
7.3.4005801059272563712.1	$x^{7} + 861 x^{3} - 5740 x^{2} + 1722 x + 2132$	$7$	[3,2]	$2^{10}\cdot 7^{7}\cdot 41^{6}$	$3$	$454.492848427$	$851.434225578093$				$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$4$	$17536829.114$
7.1.239...875.1	$x^{7} + 287 x^{5} - 861 x^{4} + 1722 x^{3} - 22099 x^{2} - 381710 x + 2072140$	$7$	[1,3]	$-\,5^{3}\cdot 7^{9}\cdot 41^{6}$	$3$	$586.812503596$	$756.4669067853504$				$D_{7}$ (as 7T2)	$[7]$	$[7]$	$2$	$3$	$7777376.25803$
7.1.385...983.1	$x^{7} - 7462 x^{4} - 97006 x^{3} - 1559558 x^{2} - 9051406 x - 62041733$	$7$	[1,3]	$-\,7^{5}\cdot 13^{6}\cdot 41^{6}$	$3$	$872.6421931553961$	$1100.1277440755782$			?	$F_7$ (as 7T4)	$[14]$	$[14]$	$2$	$3$	$9464104.459419131$
7.1.460...087.1	$x^{7} - 287$	$7$	[1,3]	$-\,7^{13}\cdot 41^{6}$	$2$	$895.063714763$	$1128.3942411333242$			✓	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$14865238.0521$
7.1.294...568.1	$x^{7} - 9184$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[14]$	$[14]$	$2$	$3$	$52530087.1756$
7.1.294...568.2	$x^{7} - 8036$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[14]$	$[14]$	$2$	$3$	$45572068.9801$
7.1.294...568.3	$x^{7} - 4592$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$99934343.5828$
7.1.294...568.4	$x^{7} - 4018$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[21]$	$[21]$	$2$	$3$	$29316853.638$
7.1.294...568.5	$x^{7} - 2296$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$97464792.8903$
7.1.294...568.6	$x^{7} - 1148$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			?	$F_7$ (as 7T4)	$[14]$	$[14]$	$2$	$3$	$61875307.7636$
7.1.294...568.7	$x^{7} - 574$	$7$	[1,3]	$-\,2^{6}\cdot 7^{13}\cdot 41^{6}$	$3$	$1621.36077497$	$2044.0267336271295$			✓	$F_7$ (as 7T4)	$[7]$	$[7]$	$2$	$3$	$93919268.2268$

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