LMFDB - 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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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. $p$

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Results (1-50 of 196 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.3.145894103.1	$x^{9} - x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{4} + x^{3} + 3 x^{2} - x - 1$	$9$	[3,3]	$-\,19\cdot 7678637$	$2$	$8.074493778509295$	$12078.663129667952$	✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$2.3315410233157543$
10.0.553343099.1	$x^{10} - 2 x^{9} + 2 x^{8} - x^{7} - x^{5} + 4 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,19\cdot 293\cdot 99397$	$3$	$7.48685547744$	$23523.24592823023$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.0598386706152494$
10.2.960883181.1	$x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - x^{5} - 3 x^{4} - x^{3} + 1$	$10$	[2,4]	$19\cdot 47\cdot 1076017$	$3$	$7.91164986734$	$30998.115765317092$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$1.8485778462930664$
10.2.1092986533.1	$x^{10} - x^{9} - x^{8} + 2 x^{7} + x^{6} - 3 x^{5} - x^{4} + 3 x^{3} + x^{2} - 2 x - 1$	$10$	[2,4]	$19\cdot 1019\cdot 56453$	$3$	$8.01422407681$	$33060.3468372611$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.0036554559775457$
10.0.1132317616.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 6 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 19\cdot 59\cdot 63131$	$4$	$8.04260660852$	$14646.981639243797$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.5714139124419537$
10.0.1155602572.1	$x^{10} - 2 x^{9} + 2 x^{8} - x^{7} - 2 x^{6} + 3 x^{5} + 2 x^{2} + 1$	$10$	[0,5]	$-\,2^{2}\cdot 19\cdot 2243\cdot 6779$	$4$	$8.05899432551$	$26981.178678622025$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.6113321617411596$
10.2.1420436789.1	$x^{10} - x^{9} + 2 x^{7} - 4 x^{6} + 3 x^{5} + 3 x^{4} - 6 x^{3} + x^{2} + 3 x - 1$	$10$	[2,4]	$19\cdot 61\cdot 1225571$	$3$	$8.22701314452$	$37688.68250549494$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.3640238159569362$
10.2.1566975581.1	$x^{10} - 3 x^{9} + 6 x^{8} - 5 x^{7} + 9 x^{5} - 16 x^{4} + 16 x^{3} - 11 x^{2} + 5 x - 1$	$10$	[2,4]	$19\cdot 53\cdot 1556083$	$3$	$8.30818623154$	$39585.04238977142$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.5237961659206753$
10.2.1589788577.1	$x^{10} - x^{9} - x^{8} + 2 x^{6} - 2 x^{4} + 2 x^{3} + x^{2} - 2 x - 1$	$10$	[2,4]	$13^{2}\cdot 19\cdot 89\cdot 5563$	$4$	$8.32020328135$	$11058.545519190126$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.5960083616543974$
10.0.1639662247.1	$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 11 x^{6} - 10 x^{5} + 9 x^{4} - 5 x^{3} + 3 x^{2} + 1$	$10$	[0,5]	$-\,19\cdot 86298013$	$2$	$8.34594348853$	$40492.74313997509$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.2650446640662443$
10.0.1648963279.1	$x^{10} + 2 x^{8} - x^{7} + 3 x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$	$10$	[0,5]	$-\,19\cdot 86787541$	$2$	$8.35066570774$	$40607.42886467943$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.2028222908298507$
10.2.1707677117.1	$x^{10} - x^{9} - 3 x^{8} + x^{7} + 4 x^{6} + 2 x^{5} - 3 x^{4} - 2 x^{3} + 2 x^{2} - x - 1$	$10$	[2,4]	$19\cdot 89877743$	$2$	$8.37993357027$	$41324.05010402538$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.7415991011387923$
10.0.1788072007.1	$x^{10} - 3 x^{9} + 6 x^{8} - 10 x^{7} + 14 x^{6} - 13 x^{5} + 8 x^{4} - 5 x^{3} + 6 x^{2} - 5 x + 2$	$10$	[0,5]	$-\,19\cdot 449\cdot 209597$	$3$	$8.41857335416$	$42285.60046871748$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.4283733478648126$
10.0.1791582067.1	$x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 2 x^{6} - 2 x^{5} + 4 x^{4} - x^{3} - x^{2} + 1$	$10$	[0,5]	$-\,11\cdot 19\cdot 8572163$	$3$	$8.42022449721$	$42327.08431961739$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.220604430253295$
10.2.1897391053.1	$x^{10} - x^{9} - x^{8} + 4 x^{7} - x^{6} - 4 x^{5} + x^{4} + 3 x^{3} - 2 x + 1$	$10$	[2,4]	$19\cdot 31\cdot 271\cdot 11887$	$4$	$8.46867925974$	$43559.052480512015$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.8177032411025302$
10.0.2092573607.1	$x^{10} - 2 x^{9} + 4 x^{7} - 4 x^{6} + 4 x^{4} - 2 x^{3} - x + 1$	$10$	[0,5]	$-\,19\cdot 89\cdot 109\cdot 11353$	$4$	$8.55200752496$	$45744.65659506037$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.9867129668152916$
10.2.2121596069.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{5} + 11 x^{4} - 11 x^{3} + 7 x^{2} - 4 x + 1$	$10$	[2,4]	$19\cdot 239\cdot 467209$	$3$	$8.56379514971$	$46060.786673698916$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.2685985356275213$
10.2.2145330413.1	$x^{10} - x^{9} + x^{8} + x^{6} - 3 x^{5} + 5 x^{4} - x^{3} - 2 x^{2} - x - 1$	$10$	[2,4]	$19\cdot 112912127$	$2$	$8.57332759704$	$46317.71165547797$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.046819537150048$
10.0.2149116391.1	$x^{10} - x^{9} - x^{7} + 2 x^{6} + x^{5} - x^{4} - x^{3} + x + 1$	$10$	[0,5]	$-\,19^{2}\cdot 139\cdot 42829$	$3$	$8.57483937731$	$17373.157942551185$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.886084763124819$
10.2.2256405629.1	$x^{10} - x^{9} + 3 x^{7} - 4 x^{6} + 2 x^{5} + 2 x^{4} - 5 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[2,4]	$19\cdot 937\cdot 126743$	$3$	$8.61671477507$	$47501.63817175151$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.143400472294802$
10.2.2258711621.1	$x^{10} - 2 x^{8} + 2 x^{6} - 2 x^{5} - 2 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$	$10$	[2,4]	$19\cdot 1913\cdot 62143$	$3$	$8.61759497777$	$47525.90473625936$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.143794748144905$
10.0.2289921667.1	$x^{10} - 2 x^{9} + 3 x^{8} - 5 x^{7} + 5 x^{6} - 5 x^{5} + 6 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,11\cdot 19\cdot 2213\cdot 4951$	$4$	$8.629429055$	$47853.12598984522$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.512756296641533$
10.0.2293895099.1	$x^{10} - 2 x^{9} + x^{8} - x^{7} + 2 x^{6} + 2 x^{5} - 3 x^{4} - x^{3} + x + 1$	$10$	[0,5]	$-\,19\cdot 29\cdot 4163149$	$3$	$8.63092525052$	$47894.62494894391$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.3410426532706667$
10.0.2304285743.1	$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 7 x^{6} - 4 x^{5} + 7 x^{4} - 3 x^{3} + 5 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,19^{2}\cdot 6383063$	$2$	$8.6348268497$	$17989.41190892089$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.5169195903949944$
10.2.2346745157.1	$x^{10} - x^{9} - 2 x^{8} + x^{7} + 5 x^{6} + x^{5} - 7 x^{4} - 5 x^{3} + 3 x^{2} + 4 x + 1$	$10$	[2,4]	$19\cdot 123512903$	$2$	$8.65060721328$	$48443.215799531725$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.3179940167401596$
10.0.2356756979.1	$x^{10} - x^{9} + 3 x^{8} - 5 x^{7} + 7 x^{6} - 8 x^{5} + 9 x^{4} - 9 x^{3} + 6 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,19\cdot 124039841$	$2$	$8.65429072$	$48546.44146587884$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.7787090872711735$
10.0.2368913027.1	$x^{10} - x^{9} + 4 x^{8} - 5 x^{7} + 9 x^{6} - 8 x^{5} + 11 x^{4} - 6 x^{3} + 6 x^{2} - x + 1$	$10$	[0,5]	$-\,13\cdot 19\cdot 719\cdot 13339$	$4$	$8.65874423755$	$48671.48063291274$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.5013075417118125$
10.0.2371660807.1	$x^{10} - x^{9} + 2 x^{8} - x^{7} + 3 x^{6} + x^{2} + 2 x + 1$	$10$	[0,5]	$-\,19\cdot 124824253$	$2$	$8.65974806987$	$48699.70027628507$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.500240086279474$
10.2.2427005413.1	$x^{10} - 2 x^{9} + x^{8} + x^{7} - 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1$	$10$	[2,4]	$7\cdot 19\cdot 18248161$	$3$	$8.67974716161$	$49264.6466850215$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.3996878836762345$
10.0.2500560227.1	$x^{10} - 2 x^{7} - x^{6} - x^{5} + 2 x^{4} + x^{2} + 1$	$10$	[0,5]	$-\,11^{2}\cdot 19\cdot 1087673$	$3$	$8.70570069566$	$22484.73453886899$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.9697891441649733$
10.0.2522777839.1	$x^{10} - 2 x^{9} + 2 x^{8} + 2 x^{6} - 5 x^{5} + 6 x^{4} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,19\cdot 23\cdot 1297\cdot 4451$	$4$	$8.71340500354$	$50227.261910241534$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.2016818139431176$
10.0.2543800199.1	$x^{10} - x^{9} + x^{8} + x^{7} + x^{5} + x^{4} + 3 x^{2} - x + 1$	$10$	[0,5]	$-\,19\cdot 1237\cdot 108233$	$3$	$8.72063881746$	$50436.1001565347$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.0813737890766495$
10.2.2707200161.1	$x^{10} - x^{9} - x^{8} + 3 x^{7} - 3 x^{5} + 5 x^{4} - 2 x^{3} - 3 x^{2} + 3 x - 1$	$10$	[2,4]	$19\cdot 1301\cdot 109519$	$3$	$8.77509923996$	$52030.76167999081$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.6174477694913154$
10.0.2714112019.1	$x^{10} - 2 x^{9} + 5 x^{8} - 7 x^{7} + 10 x^{6} - 11 x^{5} + 14 x^{4} - 11 x^{3} + 8 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,19\cdot 463\cdot 308527$	$3$	$8.77733707479$	$52097.14021901778$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.241982133997585$
10.2.2728633909.1	$x^{10} - x^{9} - 3 x^{8} + 4 x^{7} + 2 x^{6} - 5 x^{5} + 2 x^{4} + 4 x^{3} - 2 x^{2} - 2 x + 1$	$10$	[2,4]	$17\cdot 19\cdot 8447783$	$3$	$8.78202213056$	$52236.32748384978$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.4771350392795592$
10.0.2756899867.1	$x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} + 4 x^{6} - 4 x^{5} + 3 x^{4} - x + 1$	$10$	[0,5]	$-\,19\cdot 89\cdot 263\cdot 6199$	$4$	$8.79107730847$	$52506.18884474477$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.0552013268423805$
10.0.2801442859.1	$x^{10} + 2 x^{6} - 3 x^{5} - 3 x^{4} + x^{2} + 2 x + 1$	$10$	[0,5]	$-\,19\cdot 3499\cdot 42139$	$3$	$8.80517875098$	$52928.65820139407$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.468784777230629$
10.2.2863923029.1	$x^{10} + x^{8} - x^{7} - 3 x^{5} - 2 x^{3} + 2 x^{2} + 1$	$10$	[2,4]	$11\cdot 19\cdot 13702981$	$3$	$8.82462245882$	$53515.633500875236$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.7251694626980894$
10.0.2880779012.1	$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 4 x^{6} - x^{4} + 3 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 19\cdot 37904987$	$3$	$8.82980259752$	$53672.888985036014$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.647133070302393$
10.2.2939501381.1	$x^{10} - 3 x^{9} + 7 x^{8} - 9 x^{7} + 10 x^{6} - 5 x^{5} - x^{4} + 4 x^{3} - 6 x^{2} + 4 x - 1$	$10$	[2,4]	$19\cdot 154710599$	$2$	$8.84763844078$	$54217.168692214094$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.8178178802127665$
10.2.2985678373.1	$x^{10} - x^{9} - 2 x^{8} + 5 x^{7} - x^{6} - 5 x^{5} + 5 x^{4} - 3 x^{2} + x + 1$	$10$	[2,4]	$19\cdot 2663\cdot 59009$	$3$	$8.86144001979$	$54641.36137579297$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.7430876475635557$
10.0.3018472696.1	$x^{10} - x^{9} + 3 x^{8} - x^{7} + 5 x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - x + 1$	$10$	[0,5]	$-\,2^{3}\cdot 19\cdot 223\cdot 89051$	$4$	$8.87112553904$	$54940.6288278538$	?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$5.1151463884316115$
10.0.3213917887.1	$x^{10} - 2 x^{9} + x^{6} + 2 x^{5} - 3 x^{3} + 2 x + 1$	$10$	[0,5]	$-\,19\cdot 233\cdot 725981$	$3$	$8.92695771596$	$56691.426926829066$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.917858741608165$
10.0.3253853132.1	$x^{10} - x^{9} + x^{8} + x^{7} - 3 x^{6} + 4 x^{5} - x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 19\cdot 331\cdot 129347$	$4$	$8.93798856384$	$45274.70626228933$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$5.173001319399761$
10.2.3266441677.1	$x^{10} - 2 x^{7} + x^{5} - x^{4} - 6 x^{3} - 7 x^{2} - 4 x - 1$	$10$	[2,4]	$19\cdot 79\cdot 83\cdot 157\cdot 167$	$5$	$8.94144049786$	$57152.79238147511$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.886683205564635$
10.0.3292060327.1	$x^{10} - 2 x^{9} + 5 x^{8} - 5 x^{7} + 8 x^{6} - 6 x^{5} + 8 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,19\cdot 373\cdot 464521$	$3$	$8.9484286272$	$57376.47886547239$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.253336158000616$
10.2.3340705685.1	$x^{10} - 3 x^{9} + 3 x^{8} + 2 x^{7} - 8 x^{6} + 12 x^{5} - 15 x^{4} + 17 x^{3} - 13 x^{2} + 6 x - 1$	$10$	[2,4]	$5\cdot 19\cdot 35165323$	$3$	$8.9615642252$	$57798.83809385791$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.332269035789318$
10.2.3344670149.1	$x^{10} - x^{9} - x^{8} + 3 x^{7} - x^{6} - 4 x^{5} + 7 x^{4} - 5 x^{3} + x - 1$	$10$	[2,4]	$19\cdot 176035271$	$2$	$8.96262713956$	$57833.12328588177$	?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.9437509324955333$
10.2.3357745037.1	$x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 3 x^{6} - 5 x^{5} - 3 x^{4} + 5 x^{3} + x^{2} - 3 x + 1$	$10$	[2,4]	$19\cdot 176723423$	$2$	$8.96612463575$	$57946.05281639121$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.177972552850926$
10.2.3453833053.1	$x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 5 x^{6} + 8 x^{5} - 9 x^{4} + 8 x^{3} - 5 x^{2} + 3 x - 1$	$10$	[2,4]	$11\cdot 19\cdot 3853\cdot 4289$	$4$	$8.99145829291$	$58769.320678394775$	✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.024214534902702$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.