Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

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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	Unit group torsion	Unit group rank	Regulator
10.0.452203195.1	$x^{10} - x^{9} + x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 90440639$	$2$	$7.33725077262$	$21265.069832944355$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.9926098846749679$
10.0.500358335.1	$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 10 x^{6} - 7 x^{5} + 3 x^{4} - x + 1$	$10$	[0,5]	$-\,5\cdot 1997\cdot 50111$	$3$	$7.41187546868$	$22368.690954099213$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.0598010791900303$
10.0.531969835.1	$x^{10} - x^{9} + 3 x^{8} - 2 x^{7} + 5 x^{6} - 2 x^{5} + 6 x^{4} - x^{3} + 3 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 4241\cdot 25087$	$3$	$7.45742167466$	$23064.47127076621$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.1035307010553048$
10.0.583444835.1	$x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 4 x^{6} - 2 x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 73\cdot 191\cdot 8369$	$4$	$7.52661982319$	$24154.60277048662$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.1856126173308268$
10.0.701428235.1	$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 4 x^{6} - x^{5} + 2 x^{3} - x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 47\cdot 53\cdot 199\cdot 283$	$5$	$7.66652090743$	$26484.490461400233$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.3245987177931893$
10.0.713382235.1	$x^{10} - 3 x^{9} + 5 x^{8} - 6 x^{7} + 7 x^{6} - 7 x^{5} + 6 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 142676447$	$2$	$7.67948734417$	$26709.216293257276$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.332070894691037$
10.0.748285735.1	$x^{10} - x^{9} - x^{8} + x^{7} + 2 x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 149657147$	$2$	$7.71625811318$	$27354.811916735965$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.3934767560572046$
10.0.853632655.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + x^{6} - 4 x^{5} + 2 x^{4} + 3 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 170726531$	$2$	$7.81856591792$	$29216.992572816253$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.512413114376397$
10.0.857107435.1	$x^{10} - 4 x^{9} + 8 x^{8} - 11 x^{7} + 11 x^{6} - 9 x^{5} + 7 x^{4} - 5 x^{3} + 3 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 1583\cdot 108289$	$3$	$7.82174271292$	$29276.3972339494$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.5049029297979362$
10.0.862298235.1	$x^{10} - x^{9} + x^{8} + x^{6} - 2 x^{5} + 4 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{2}\cdot 5\cdot 3659\cdot 5237$	$4$	$7.82646684358$	$16953.841600062213$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.507749038841807$
10.0.887304895.1	$x^{10} - 2 x^{9} + x^{8} + x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 177460979$	$2$	$7.8488727429$	$29787.66346996689$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.5672885360514162$
10.0.891258635.1	$x^{10} - x^{9} + x^{8} - 4 x^{7} + 3 x^{6} - 2 x^{5} + 6 x^{4} - 3 x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 43\cdot 4145389$	$3$	$7.85236312739$	$29853.955098110535$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.532637929384105$
10.0.958058995.1	$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + 3 x^{5} - 3 x^{4} + x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 191611799$	$2$	$7.90932142836$	$30952.52808737923$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.6065226744636487$
10.0.1014444235.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{3} - x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 7\cdot 28984121$	$3$	$7.95468190966$	$31850.341206963545$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.7047478448355062$
10.0.1061546795.2	$x^{10} - 2 x^{9} + x^{8} - 2 x^{7} + 4 x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 31\cdot 2617^{2}$	$3$	$7.99086722109$	$636.8948107811839$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.67262198543$
10.0.1113203435.1	$x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - x + 1$	$10$	[0,5]	$-\,5\cdot 17^{2}\cdot 733\cdot 1051$	$4$	$8.02892597399$	$8092.129200649233$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.7648236639977228$
10.0.1189086935.1	$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 6 x^{6} - 6 x^{5} + 5 x^{4} - 4 x^{3} + 4 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 237817387$	$2$	$8.08204679611$	$34483.139865737285$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.86666887640241$
10.0.1195692335.1	$x^{10} - 3 x^{9} + 6 x^{8} - 8 x^{7} + 6 x^{6} - x^{5} - 3 x^{4} + 5 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 181\cdot 1033\cdot 1279$	$4$	$8.08652520455$	$34578.78446388768$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.0557560775979633$
10.0.1218623995.1	$x^{10} - x^{9} + 3 x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 19\cdot 523\cdot 24527$	$4$	$8.10190175445$	$34908.795381679956$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.8391860483849705$
10.0.1246572335.1	$x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + 3 x^{6} - 2 x^{4} + 3 x^{3} - x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 167\cdot 1492901$	$3$	$8.12029390709$	$35306.83127951303$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.9245076161598238$
10.0.1273745135.1	$x^{10} - 3 x^{9} + 4 x^{8} - 2 x^{7} + 3 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 13\cdot 19596079$	$3$	$8.13782326675$	$35689.566192376165$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.9141392897321539$
10.0.1274853395.1	$x^{10} - x^{7} + 2 x^{6} - x^{5} - 2 x^{4} - x^{3} + x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 254970679$	$2$	$8.13853104529$	$35705.0892030814$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.978851132317426$
10.0.1302347755.1	$x^{10} - 3 x^{9} + 6 x^{8} - 10 x^{7} + 15 x^{6} - 17 x^{5} + 15 x^{4} - 11 x^{3} + 7 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 1093\cdot 238307$	$3$	$8.15591510536$	$36088.05557244668$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.8946428461351785$
10.0.1318100335.1	$x^{10} - x^{8} - x^{7} - x^{6} + 2 x^{5} + 4 x^{4} - x^{3} - 3 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 263620067$	$2$	$8.16572682563$	$36305.6515572989$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.9689669288254044$
10.0.1410854795.1	$x^{10} + 4 x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 7^{2}\cdot 31\cdot 431^{2}$	$4$	$8.22144643999$	$683.8384312101799$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$2.16081245683$
10.0.1509650695.1	$x^{10} - x^{9} + x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{3} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 7\cdot 107\cdot 491\cdot 821$	$5$	$8.27728001082$	$38854.22364428351$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.230962166772597$
10.0.1533949635.1	$x^{10} + 2 x^{8} - x^{7} + 3 x^{6} - 3 x^{5} + 4 x^{4} - 5 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,3\cdot 5\cdot 29\cdot 269\cdot 13109$	$5$	$8.29050737631$	$39165.66908658653$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.619339148587336$
10.0.1578373835.1	$x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} + x^{6} + 2 x^{5} - 3 x^{4} + x^{3} + 2 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 31\cdot 10183057$	$3$	$8.31420995386$	$39728.7532525248$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2199032192037875$
10.0.1586662235.1	$x^{10} - 2 x^{9} + x^{8} + x^{7} - x^{6} + 2 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 16183\cdot 19609$	$3$	$8.31856565175$	$39832.92902863157$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.175772096553176$
10.0.1595326955.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 3 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 319065391$	$2$	$8.32309727313$	$39941.54422402819$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.1516035174155532$
10.0.1600697255.1	$x^{10} - x^{9} + 2 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 2 x^{4} - x^{3} + 3 x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 53\cdot 6040367$	$3$	$8.32589481657$	$40008.71473816673$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.4656347026264167$
10.0.1603885635.1	$x^{10} - 3 x^{9} + 3 x^{8} + 2 x^{7} - 6 x^{6} + 3 x^{5} + 5 x^{4} - 9 x^{3} + 8 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{2}\cdot 5\cdot 11\cdot 1487\cdot 2179$	$5$	$8.32755174151$	$23122.03591814527$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.219128692681599$
10.0.1609573535.1	$x^{10} - x^{5} - x^{4} + x^{3} + 1$	$10$	[0,5]	$-\,5\cdot 11171\cdot 28817$	$3$	$8.33050025982$	$40119.49071212146$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.327946509278152$
10.0.1610494135.1	$x^{10} - x^{9} + 2 x^{8} + 2 x^{6} - 2 x^{5} + 3 x^{4} - x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 3917\cdot 82231$	$3$	$8.33097660248$	$40130.96229845479$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.4892533666137115$
10.0.1615958395.1	$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{4} - 3 x^{3} + 5 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 3631\cdot 89009$	$3$	$8.33379892054$	$40198.98499962406$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2873648809713107$
10.0.1635801935.1	$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 4 x^{6} - 5 x^{5} + 6 x^{4} - 7 x^{3} + 7 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,5\cdot 521\cdot 627947$	$3$	$8.34397649013$	$40445.04833721923$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.1570235835805214$
10.0.1651859135.1	$x^{10} + x^{8} - x^{7} + x^{6} - x^{5} + x + 1$	$10$	[0,5]	$-\,5\cdot 89\cdot 3712043$	$3$	$8.35213106699$	$40643.069950484794$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.7469531095643576$
10.0.1674213395.1	$x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} + 2 x^{6} - x^{5} + 3 x^{4} - 5 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,5\cdot 334842679$	$2$	$8.36336558232$	$40917.15282128022$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2927561099991136$
10.0.1704412495.1	$x^{10} - x^{7} - x^{6} - x^{5} + 2 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 271\cdot 1257869$	$3$	$8.3783301712$	$41284.530940777324$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.395547379903939$
10.2.1725803645.1	$x^{10} - 3 x^{9} + 4 x^{8} - 2 x^{7} - 2 x^{6} + 5 x^{5} - 6 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$	$10$	[2,4]	$5\cdot 83\cdot 1151\cdot 3613$	$4$	$8.38878643678$	$41542.792936922284$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.872620221066213$
10.0.1752717535.1	$x^{10} - 2 x^{9} + 2 x^{8} - 3 x^{6} + 5 x^{5} - 3 x^{4} - x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 350543507$	$2$	$8.40177782892$	$41865.46948261777$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2382678981522006$
10.0.1759648355.1	$x^{10} - 2 x^{9} + 3 x^{8} - x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,5\cdot 1033\cdot 340687$	$3$	$8.40509427028$	$41948.16271304382$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2724125554333305$
10.0.1764468955.1	$x^{10} - 3 x^{9} + 3 x^{8} - 2 x^{6} + x^{4} - x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 352893791$	$2$	$8.40739403286$	$42005.58242662515$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.324074670364796$
10.0.1775331655.1	$x^{10} - x^{9} - 3 x^{8} + 2 x^{7} + 4 x^{6} - 2 x^{5} - 4 x^{4} + 4 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,5\cdot 355066331$	$2$	$8.41255564096$	$42134.68470274816$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.3339561658843437$
10.2.1778248565.1	$x^{10} - 3 x^{9} + 2 x^{8} + 4 x^{7} - 9 x^{6} + 7 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + x + 1$	$10$	[2,4]	$5\cdot 23\cdot 167\cdot 92593$	$4$	$8.41393682197$	$42169.284615701035$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.922104956179011$
10.0.1793266595.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - 4 x^{5} + 7 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,5\cdot 367\cdot 977257$	$3$	$8.42101587073$	$42346.9785817123$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.4166123805237048$
10.0.1800524615.1	$x^{10} - x^{9} - x^{6} - x^{3} + 2 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 360104923$	$2$	$8.42441797879$	$42432.589067837944$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.440161843073263$
10.0.1806882035.1	$x^{10} - x^{9} + x^{8} + 2 x^{7} + 2 x^{5} + x^{4} + 2 x^{3} + 3 x^{2} + x + 1$	$10$	[0,5]	$-\,5\cdot 7\cdot 51625201$	$3$	$8.42738781634$	$42507.43505552882$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.436559040540062$
10.0.1810230595.1	$x^{10} - x^{9} - x^{8} + 3 x^{7} - 3 x^{5} + 3 x^{3} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 839\cdot 431521$	$3$	$8.42894830047$	$42546.80475664418$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.406757738590436$
10.0.1815342695.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - x^{4} + x^{3} - 2 x^{2} + 1$	$10$	[0,5]	$-\,5\cdot 349\cdot 1040311$	$3$	$8.43132562003$	$42606.83859429141$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.4285638186847116$

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