LMFDB - Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Refine search

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. $p$

		Sort order	Select

Results (1-50 of 759818 matches)

Next Download displayed columns for results to

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.0.30060272.1	$x^{6} - x^{5} + 17 x^{4} - 11 x^{3} + 112 x^{2} - 88 x + 308$	$6$	[0,3]	$-\,2^{4}\cdot 11^{2}\cdot 15527$	$3$	$17.6332413159$	$656.0346569486929$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$6.48809002326$
6.0.31055216.1	$x^{6} - 3 x^{5} + 17 x^{4} - 29 x^{3} + 62 x^{2} - 48 x + 16$	$6$	[0,3]	$-\,2^{4}\cdot 79^{2}\cdot 311$	$3$	$17.7291980868$	$313.49003173944783$	✓		$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$15.6538339685$
6.0.31504463.2	$x^{6} - 3 x^{5} + x^{4} - x^{3} - 57 x^{2} + 207 x + 459$	$6$	[0,3]	$-\,31^{2}\cdot 32783$	$2$	$17.771688003$	$1008.1036653043178$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$3.60621637861$
6.0.31594759.1	$x^{6} - 2 x^{5} + 19 x^{4} - 28 x^{3} + 122 x^{2} - 106 x + 281$	$6$	[0,3]	$-\,7^{4}\cdot 13159$	$2$	$17.7801672213$	$419.76878163902694$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.33559808.1	$x^{6} - 2 x^{5} - 4 x^{4} - 8 x^{3} + 26 x^{2} + 72 x + 40$	$6$	[0,3]	$-\,2^{8}\cdot 337\cdot 389$	$3$	$17.9598723085$	$1024.0820279645573$		?	$C_3^2:D_4$ (as 6T13)	$[11]$	$4$	$2$	$16.9796142315$
6.0.34082471.1	$x^{6} - 2 x^{5} + 17 x^{4} - 21 x^{3} + 98 x^{2} - 53 x + 176$	$6$	[0,3]	$-\,59^{2}\cdot 9791$	$2$	$18.0061907117$	$760.0453933812112$			$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$7.40510674034$
6.0.34148336.1	$x^{6} - x^{5} + 9 x^{4} - 13 x^{3} + 30 x^{2} - 50 x + 86$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 1559$	$3$	$18.0119855963$	$381.2506417596854$	✓	?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$6.64934608307$
6.0.34250608.1	$x^{6} - x^{5} - 3 x^{4} + x^{3} + 28 x^{2} + 2 x + 64$	$6$	[0,3]	$-\,2^{4}\cdot 7^{3}\cdot 79^{2}$	$3$	$18.0209651808$	$47.031904065219386$	✓		$D_{6}$ (as 6T3)	$[11]$	$2$	$2$	$15.6538339685$
6.0.35199728.1	$x^{6} - x^{5} + 9 x^{4} - 5 x^{3} + 24 x^{2} - 2 x + 50$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 1607$	$3$	$18.1032500974$	$387.0753045744439$	✓	?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$6.64934608307$
6.0.36081503.3	$x^{6} - x^{5} + 28 x^{4} - 15 x^{3} + 290 x^{2} - 16 x + 1049$	$6$	[0,3]	$-\,23^{2}\cdot 68207$	$2$	$18.1780559869$	$1252.5018962061495$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$2.76054002331$
6.0.36300719.1	$x^{6} - x^{5} + 19 x^{4} - 13 x^{3} + 119 x^{2} - 49 x + 301$	$6$	[0,3]	$-\,7^{4}\cdot 13\cdot 1163$	$3$	$18.196416596$	$449.94582547941286$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$2.10181872849$
6.0.37242880.1	$x^{6} - 2 x^{5} - 5 x^{4} + 32 x^{3} - 16 x^{2} - 76 x + 170$	$6$	[0,3]	$-\,2^{11}\cdot 5\cdot 3637$	$3$	$18.2742912781$	$907.1709630583155$		?	$C_3^2:D_4$ (as 6T13)	$[11]$	$4$	$2$	$15.5377579856$
6.0.38198560.1	$x^{6} - x^{5} + 10 x^{4} - 3 x^{3} + 33 x^{2} + 2 x + 46$	$6$	[0,3]	$-\,2^{5}\cdot 5\cdot 193\cdot 1237$	$4$	$18.3516238313$	$4370.272302728973$		?	$S_6$ (as 6T16)	$[11]$	$2$	$2$	$9.46789251925$
6.0.38317559.1	$x^{6} - 2 x^{5} + 22 x^{4} - 32 x^{3} + 143 x^{2} - 130 x + 349$	$6$	[0,3]	$-\,7^{4}\cdot 15959$	$2$	$18.3611398776$	$462.27619581917895$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.38353904.1	$x^{6} - 3 x^{5} + 11 x^{4} - 15 x^{3} + 38 x^{2} - 18 x + 50$	$6$	[0,3]	$-\,2^{4}\cdot 17\cdot 37^{2}\cdot 103$	$4$	$18.3640413848$	$404.0458020065031$	✓	?	$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$2$	$6.64934608307$
6.0.38404871.2	$x^{6} - x^{5} + 12 x^{4} + 19 x^{3} + 36 x^{2} + 286 x + 1127$	$6$	[0,3]	$-\,19\cdot 23^{2}\cdot 3821$	$3$	$18.3681063438$	$1292.1985141610403$		?	$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$2$	$2.89363302717$
6.0.38720927.1	$x^{6} - 2 x^{5} + 20 x^{4} - 20 x^{3} + 133 x^{2} - 56 x + 301$	$6$	[0,3]	$-\,7^{4}\cdot 16127$	$2$	$18.3932140238$	$464.70301084885625$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.38729583.1	$x^{6} + 15 x^{4} - 10 x^{3} + 72 x^{2} - 72 x + 153$	$6$	[0,3]	$-\,3^{8}\cdot 5903$	$2$	$18.3938992554$	$332.42835809731775$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$3.39714980258$
6.0.39054832.1	$x^{6} - 3 x^{5} + 17 x^{4} - 29 x^{3} + 66 x^{2} - 52 x + 40$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 1783$	$3$	$18.4195547953$	$407.72110954085923$	✓	?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$6.64934608307$
6.0.39272896.1	$x^{6} - x^{5} + x^{4} - 5 x^{3} + 2 x^{2} - 14 x + 104$	$6$	[0,3]	$-\,2^{6}\cdot 13^{2}\cdot 3631$	$3$	$18.4366560891$	$614.5111878558437$			$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$15.829439091$
6.0.39662119.1	$x^{6} - 3 x^{5} + 25 x^{4} - 45 x^{3} + 167 x^{2} - 145 x + 293$	$6$	[0,3]	$-\,7^{4}\cdot 16519$	$2$	$18.466984537$	$470.31688408722863$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.39674367.1	$x^{6} - 3 x^{5} + 18 x^{4} - 27 x^{3} + 78 x^{2} - 48 x + 152$	$6$	[0,3]	$-\,3^{8}\cdot 6047$	$2$	$18.467934875$	$336.45861840938744$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$3.39714980258$
6.0.39761375.1	$x^{6} - x^{5} - 12 x^{4} + 39 x^{3} - 44 x^{2} - 268 x + 744$	$6$	[0,3]	$-\,5^{3}\cdot 31^{2}\cdot 331$	$3$	$18.4746789093$	$226.5060705588263$		?	$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$2$	$3.80518799477$
6.0.40361039.1	$x^{6} - 3 x^{5} - 9 x^{4} + 23 x^{3} - 48 x^{2} + 36 x + 648$	$6$	[0,3]	$-\,31^{2}\cdot 41999$	$2$	$18.520827619$	$1141.0385620126956$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$3.5323605617$
6.0.40430231.1	$x^{6} - 2 x^{5} - 11 x^{4} - 15 x^{3} + 14 x^{2} + 272 x + 632$	$6$	[0,3]	$-\,31^{2}\cdot 42071$	$2$	$18.5261156341$	$1142.0161995348403$		?	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$3.52533401596$
6.0.41434343.1	$x^{6} - 2 x^{5} - 11 x^{4} + 27 x^{3} + 22 x^{2} - 173 x + 272$	$6$	[0,3]	$-\,59^{2}\cdot 11903$	$2$	$18.6020186797$	$838.0196895061595$			$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$8.2029215321$
6.0.41468111.1	$x^{6} - 3 x^{5} + 27 x^{4} - 49 x^{3} + 249 x^{2} - 225 x + 729$	$6$	[0,3]	$-\,31^{2}\cdot 43151$	$2$	$18.6045445223$	$1156.581601098686$		?	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$3.58325005728$
6.0.41680439.1	$x^{6} - x^{5} - 7 x^{4} - 21 x^{3} - 121 x^{2} + 263 x + 1243$	$6$	[0,3]	$-\,23^{2}\cdot 78791$	$2$	$18.6203874766$	$1346.1771800175488$		?	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$2.77451431226$
6.0.42332167.1	$x^{6} - 2 x^{5} + 12 x^{4} - 44 x^{3} + 117 x^{2} - 356 x + 1393$	$6$	[0,3]	$-\,23^{2}\cdot 43\cdot 1861$	$3$	$18.6685999857$	$1356.6609745990338$		?	$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$2$	$2.79645962112$
6.0.42398359.1	$x^{6} - 2 x^{5} + 20 x^{4} - 31 x^{3} + 200 x^{2} - 63 x + 811$	$6$	[0,3]	$-\,31^{2}\cdot 44119$	$2$	$18.6734619608$	$1169.482364125257$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$3.5716197794$
6.0.43453503.1	$x^{6} - 3 x^{5} + 18 x^{4} - 27 x^{3} + 96 x^{2} - 84 x + 152$	$6$	[0,3]	$-\,3^{8}\cdot 37\cdot 179$	$3$	$18.7501234796$	$352.118668122914$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$3.39714980258$
6.0.43619904.1	$x^{6} - 2 x^{5} - 14 x^{4} + 24 x^{3} + 48 x^{2} - 54 x + 81$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 25243$	$3$	$18.7620713948$	$1100.7561037759453$			$C_3^2:D_4$ (as 6T13)	$[11]$	$6$	$2$	$21.9952561517$
6.0.44771447.1	$x^{6} - 3 x^{5} + 25 x^{4} - 45 x^{3} + 174 x^{2} - 152 x + 328$	$6$	[0,3]	$-\,7^{4}\cdot 29\cdot 643$	$3$	$18.8437292307$	$499.69290004571525$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$2.10181872849$
6.0.45194023.1	$x^{6} - x^{5} + 22 x^{4} - x^{3} + 148 x^{2} + 20 x + 344$	$6$	[0,3]	$-\,7^{5}\cdot 2689$	$2$	$18.8732561273$	$262.44830229925736$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$2.10181872849$
6.0.45578183.1	$x^{6} - x^{5} + 23 x^{4} - 11 x^{3} + 145 x^{2} - x + 377$	$6$	[0,3]	$-\,7^{4}\cdot 41\cdot 463$	$3$	$18.8998997818$	$504.1747797123313$	✓	?	$A_4\times C_2$ (as 6T6)	$[14]$	$2$	$2$	$2.10181872849$
6.0.46116007.1	$x^{6} - x^{5} + 24 x^{4} - 35 x^{3} + 180 x^{2} - 156 x + 379$	$6$	[0,3]	$-\,7^{4}\cdot 19207$	$2$	$18.9368882387$	$507.14069506653175$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.47220976.2	$x^{6} - x^{5} + 15 x^{4} - 11 x^{3} + 122 x^{2} - 120 x + 406$	$6$	[0,3]	$-\,2^{4}\cdot 11^{2}\cdot 24391$	$3$	$19.0117674406$	$822.238502635147$		?	$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$6.21062395924$
6.0.47595023.1	$x^{6} - 3 x^{5} + 27 x^{4} - 49 x^{3} + 195 x^{2} - 171 x + 351$	$6$	[0,3]	$-\,7^{4}\cdot 43\cdot 461$	$3$	$19.0367843481$	$515.2089322330112$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$2.10181872849$
6.0.48451639.1	$x^{6} - 2 x^{5} - 2 x^{4} + 19 x^{3} - 66 x^{2} + 319 x + 1403$	$6$	[0,3]	$-\,23^{2}\cdot 91591$	$2$	$19.0934648248$	$1451.41069308449$		?	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$2.83566823257$
6.0.48574631.1	$x^{6} - x^{5} + 21 x^{4} - 5 x^{3} + 147 x^{2} + 19 x + 377$	$6$	[0,3]	$-\,7^{4}\cdot 20231$	$2$	$19.1015342576$	$520.4839818002831$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.49594599.1	$x^{6} - 3 x^{5} + 21 x^{4} - 29 x^{3} + 111 x^{2} - 9 x + 159$	$6$	[0,3]	$-\,3^{8}\cdot 7559$	$2$	$19.1678056472$	$376.1783919446252$	✓	?	$A_4\times C_2$ (as 6T6)	$[13]$	$2$	$2$	$3.39714980258$
6.0.50094448.1	$x^{6} - 3 x^{5} + 15 x^{4} - 25 x^{3} + 56 x^{2} - 44 x + 46$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 2287$	$3$	$19.199869016$	$461.7645705791086$	✓	✓	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$6.64934608307$
6.0.50188103.2	$x^{6} - 2 x^{5} + 24 x^{4} - 16 x^{3} + 165 x^{2} - 16 x + 377$	$6$	[0,3]	$-\,7^{4}\cdot 20903$	$2$	$19.2058469392$	$529.0576562100191$	✓	?	$A_4\times C_2$ (as 6T6)	$[11]$	$2$	$2$	$2.10181872849$
6.0.50817856.2	$x^{6} + 34 x^{4} + 389 x^{2} + 1501$	$6$	[0,3]	$-\,2^{6}\cdot 19\cdot 23^{2}\cdot 79$	$4$	$19.2458039011$	$371.6073196265111$		?	$S_4\times C_2$ (as 6T11)	$[2, 6]$	$2$	$2$	$2.85193246555$
6.0.51247971.1	$x^{6} + 15 x^{4} - 10 x^{3} + 81 x^{2} - 45 x + 171$	$6$	[0,3]	$-\,3^{8}\cdot 73\cdot 107$	$3$	$19.2728576009$	$382.3974538052337$	✓	?	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$3.39714980258$
6.0.51522831.1	$x^{6} - 2 x^{5} + 12 x^{4} - 15 x^{3} + 74 x^{2} - 64 x + 160$	$6$	[0,3]	$-\,3^{3}\cdot 83^{2}\cdot 277$	$3$	$19.2900470235$	$262.6271120809883$			$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$2$	$11.0332793037$
6.0.52032071.1	$x^{6} - 3 x^{5} + 25 x^{4} - 45 x^{3} + 181 x^{2} - 159 x + 377$	$6$	[0,3]	$-\,7^{4}\cdot 13\cdot 1667$	$3$	$19.3216933554$	$538.6890769572213$	✓	✓	$A_4\times C_2$ (as 6T6)	$[12]$	$2$	$2$	$2.10181872849$
6.0.52197232.1	$x^{6} - 3 x^{5} + 13 x^{4} - 13 x^{3} + 40 x^{2} - 20 x + 68$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 2383$	$3$	$19.3319017316$	$471.35655058624326$	✓	?	$S_4\times C_2$ (as 6T11)	$[13]$	$2$	$2$	$6.64934608307$
6.0.52287583.1	$x^{6} - 2 x^{5} - x^{4} - 17 x^{3} + 10 x^{2} + 59 x + 62$	$6$	[0,3]	$-\,107^{2}\cdot 4567$	$2$	$19.3374748184$	$699.0486392233375$			$S_4\times C_2$ (as 6T11)	$[11]$	$2$	$2$	$10.8106529734$
6.0.52624112.1	$x^{6} - x^{5} + 8 x^{4} - 6 x^{3} + 32 x^{2} - 16 x + 64$	$6$	[0,3]	$-\,2^{4}\cdot 17\cdot 31\cdot 79^{2}$	$4$	$19.3581624509$	$408.0833248247225$	✓		$S_4\times C_2$ (as 6T11)	$[14]$	$2$	$2$	$15.6538339685$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 759818 matches)

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