LMFDB - Number field search results

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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 86554 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	Unit group torsion	Unit group rank	Regulator
2.0.119.1	$x^{2} - x + 30$	$2$	[0,1]	$-\,7\cdot 17$	$2$	$10.9087121146$	$10.908712114635714$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.143.1	$x^{2} - x + 36$	$2$	[0,1]	$-\,11\cdot 13$	$2$	$11.9582607431$	$11.958260743101398$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.159.1	$x^{2} - x + 40$	$2$	[0,1]	$-\,3\cdot 53$	$2$	$12.6095202129$	$12.609520212918492$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.296.1	$x^{2} + 74$	$2$	[0,1]	$-\,2^{3}\cdot 37$	$2$	$17.2046505341$	$17.204650534085253$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.303.1	$x^{2} - x + 76$	$2$	[0,1]	$-\,3\cdot 101$	$2$	$17.4068951855$	$17.406895185529212$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.319.1	$x^{2} - x + 80$	$2$	[0,1]	$-\,11\cdot 29$	$2$	$17.8605710995$	$17.86057109949175$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.344.1	$x^{2} + 86$	$2$	[0,1]	$-\,2^{3}\cdot 43$	$2$	$18.547236991$	$18.547236990991408$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.415.1	$x^{2} - x + 104$	$2$	[0,1]	$-\,5\cdot 83$	$2$	$20.3715487875$	$20.37154878746336$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.488.1	$x^{2} + 122$	$2$	[0,1]	$-\,2^{3}\cdot 61$	$2$	$22.0907220344$	$22.090722034374522$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.611.1	$x^{2} - x + 153$	$2$	[0,1]	$-\,13\cdot 47$	$2$	$24.7184141886$	$24.71841418861655$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.635.1	$x^{2} - x + 159$	$2$	[0,1]	$-\,5\cdot 127$	$2$	$25.1992063367$	$25.199206336708304$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.664.1	$x^{2} + 166$	$2$	[0,1]	$-\,2^{3}\cdot 83$	$2$	$25.7681974535$	$25.768197453450252$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.699.1	$x^{2} - x + 175$	$2$	[0,1]	$-\,3\cdot 233$	$2$	$26.4386081328$	$26.43860813280457$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.724.1	$x^{2} + 181$	$2$	[0,1]	$-\,2^{2}\cdot 181$	$2$	$26.9072480941$	$26.90724809414742$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.779.1	$x^{2} - x + 195$	$2$	[0,1]	$-\,19\cdot 41$	$2$	$27.9105714739$	$27.910571473905726$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.788.1	$x^{2} + 197$	$2$	[0,1]	$-\,2^{2}\cdot 197$	$2$	$28.0713376952$	$28.071337695236398$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.803.1	$x^{2} - x + 201$	$2$	[0,1]	$-\,11\cdot 73$	$2$	$28.3372546306$	$28.337254630609507$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.851.1	$x^{2} - x + 213$	$2$	[0,1]	$-\,23\cdot 37$	$2$	$29.1719042916$	$29.171904291629644$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.872.1	$x^{2} + 218$	$2$	[0,1]	$-\,2^{3}\cdot 109$	$2$	$29.5296461205$	$29.5296461204668$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.916.1	$x^{2} + 229$	$2$	[0,1]	$-\,2^{2}\cdot 229$	$2$	$30.2654919008$	$30.265491900843113$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.923.1	$x^{2} - x + 231$	$2$	[0,1]	$-\,13\cdot 71$	$2$	$30.3809150619$	$30.380915061926625$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1115.1	$x^{2} - x + 279$	$2$	[0,1]	$-\,5\cdot 223$	$2$	$33.3916157141$	$33.391615714128$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1268.1	$x^{2} + 317$	$2$	[0,1]	$-\,2^{2}\cdot 317$	$2$	$35.6089876295$	$35.608987629529715$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1384.1	$x^{2} + 346$	$2$	[0,1]	$-\,2^{3}\cdot 173$	$2$	$37.2021504755$	$37.20215047547655$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1492.1	$x^{2} + 373$	$2$	[0,1]	$-\,2^{2}\cdot 373$	$2$	$38.6264158317$	$38.62641583165593$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1576.1	$x^{2} + 394$	$2$	[0,1]	$-\,2^{3}\cdot 197$	$2$	$39.6988664826$	$39.698866482558415$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1643.1	$x^{2} - x + 411$	$2$	[0,1]	$-\,31\cdot 53$	$2$	$40.533936399$	$40.53393639902249$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1684.1	$x^{2} + 421$	$2$	[0,1]	$-\,2^{2}\cdot 421$	$2$	$41.0365690574$	$41.036569057366385$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1688.1	$x^{2} + 422$	$2$	[0,1]	$-\,2^{3}\cdot 211$	$2$	$41.0852771683$	$41.08527716834828$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1707.1	$x^{2} - x + 427$	$2$	[0,1]	$-\,3\cdot 569$	$2$	$41.3158565202$	$41.31585652022719$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1779.1	$x^{2} - x + 445$	$2$	[0,1]	$-\,3\cdot 593$	$2$	$42.1781934179$	$42.17819341792628$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1819.1	$x^{2} - x + 455$	$2$	[0,1]	$-\,17\cdot 107$	$2$	$42.6497362243$	$42.649736224272246$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1835.1	$x^{2} - x + 459$	$2$	[0,1]	$-\,5\cdot 367$	$2$	$42.8368999812$	$42.83689998120779$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1891.1	$x^{2} - x + 473$	$2$	[0,1]	$-\,31\cdot 61$	$2$	$43.4856298103$	$43.485629810317796$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.1923.1	$x^{2} - x + 481$	$2$	[0,1]	$-\,3\cdot 641$	$2$	$43.8520238986$	$43.8520238985614$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2152.1	$x^{2} + 538$	$2$	[0,1]	$-\,2^{3}\cdot 269$	$2$	$46.389654019$	$46.389654018972806$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2164.1	$x^{2} + 541$	$2$	[0,1]	$-\,2^{2}\cdot 541$	$2$	$46.5188133985$	$46.51881339845203$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2363.1	$x^{2} - x + 591$	$2$	[0,1]	$-\,17\cdot 139$	$2$	$48.6106984109$	$48.61069841094653$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2452.1	$x^{2} + 613$	$2$	[0,1]	$-\,2^{2}\cdot 613$	$2$	$49.5176736126$	$49.51767361255979$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2643.1	$x^{2} - x + 661$	$2$	[0,1]	$-\,3\cdot 881$	$2$	$51.4101157361$	$51.41011573610781$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2776.1	$x^{2} + 694$	$2$	[0,1]	$-\,2^{3}\cdot 347$	$2$	$52.6877594893$	$52.687759489277965$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2836.1	$x^{2} + 709$	$2$	[0,1]	$-\,2^{2}\cdot 709$	$2$	$53.2541078228$	$53.25410782277739$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.2899.1	$x^{2} - x + 725$	$2$	[0,1]	$-\,13\cdot 223$	$2$	$53.8423625039$	$53.842362503887216$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.3028.1	$x^{2} + 757$	$2$	[0,1]	$-\,2^{2}\cdot 757$	$2$	$55.0272659688$	$55.02726596879042$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.3091.1	$x^{2} - x + 773$	$2$	[0,1]	$-\,11\cdot 281$	$2$	$55.5967624957$	$55.59676249567055$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.2.3129.1	$x^{2} - x - 782$	$2$	[2,0]	$3\cdot 7\cdot 149$	$3$	$55.9374650838$	$55.937465083787984$		✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	$1$	$7.48997058673$
2.0.3139.1	$x^{2} - x + 785$	$2$	[0,1]	$-\,43\cdot 73$	$2$	$56.0267793113$	$56.02677931132576$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.3147.1	$x^{2} - x + 787$	$2$	[0,1]	$-\,3\cdot 1049$	$2$	$56.098128311$	$56.098128311023$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.3291.1	$x^{2} - x + 823$	$2$	[0,1]	$-\,3\cdot 1097$	$2$	$57.3672380371$	$57.367238037053866$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$
2.0.3412.1	$x^{2} + 853$	$2$	[0,1]	$-\,2^{2}\cdot 853$	$2$	$58.412327466$	$58.412327466040935$	✓	✓	✓	$C_2$ (as 2T1)	$[10]$	$2$	0	$1$

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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.