LMFDB - Number field search results

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Degree	Signature	Discriminant	Root discriminant	Galois root discriminant

Ramified prime count	Ramified	Unramified primes	Maximum ramified prime	Galois group

Class group structure	Class number	Regulator	Intermediate field	Field is

Narrow class group	Narrow class number	Relative class number	CM field	$p$-adic completions

Monogenic	Index	Ines. $p$	Minimal sibling	Unit signature rank

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Results (1-50 of 10478 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	Unit signature rank	Max $p$
2.0.431.1	$x^{2} - x + 108$	$2$	(0, 1)	$-\,431$	$1$	$20.760539492$	$20.760539492026695$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$431$
2.0.503.1	$x^{2} - x + 126$	$2$	(0, 1)	$-\,503$	$1$	$22.427661492$	$22.427661492005804$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$503$
2.0.743.1	$x^{2} - x + 186$	$2$	(0, 1)	$-\,743$	$1$	$27.2580263409$	$27.258026340878022$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$743$
2.0.863.1	$x^{2} - x + 216$	$2$	(0, 1)	$-\,863$	$1$	$29.3768616431$	$29.376861643136763$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$863$
2.0.1931.1	$x^{2} - x + 483$	$2$	(0, 1)	$-\,1931$	$1$	$43.9431450854$	$43.94314508543966$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$1931$
2.0.2503.1	$x^{2} - x + 626$	$2$	(0, 1)	$-\,2503$	$1$	$50.0299910054$	$50.02999100539596$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$2503$
2.0.2579.1	$x^{2} - x + 645$	$2$	(0, 1)	$-\,2579$	$1$	$50.7838557024$	$50.78385570237849$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$2579$
2.0.2767.1	$x^{2} - x + 692$	$2$	(0, 1)	$-\,2767$	$1$	$52.6022813193$	$52.602281319349636$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$2767$
2.0.2819.1	$x^{2} - x + 705$	$2$	(0, 1)	$-\,2819$	$1$	$53.0942558098$	$53.094255809833136$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$2819$
2.0.3011.1	$x^{2} - x + 753$	$2$	(0, 1)	$-\,3011$	$1$	$54.8725796733$	$54.872579673275794$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$3011$
2.0.3371.1	$x^{2} - x + 843$	$2$	(0, 1)	$-\,3371$	$1$	$58.060313468$	$58.06031346797914$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$3371$
2.0.4283.1	$x^{2} - x + 1071$	$2$	(0, 1)	$-\,4283$	$1$	$65.4446330878$	$65.4446330878247$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$4283$
2.0.4523.1	$x^{2} - x + 1131$	$2$	(0, 1)	$-\,4523$	$1$	$67.2532527094$	$67.2532527094415$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$4523$
2.0.4691.1	$x^{2} - x + 1173$	$2$	(0, 1)	$-\,4691$	$1$	$68.4908753047$	$68.49087530467106$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$4691$
2.0.5011.1	$x^{2} - x + 1253$	$2$	(0, 1)	$-\,5011$	$1$	$70.7884171316$	$70.78841713161836$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$5011$
2.0.5647.1	$x^{2} - x + 1412$	$2$	(0, 1)	$-\,5647$	$1$	$75.146523539$	$75.14652353901675$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$5647$
2.0.5851.1	$x^{2} - x + 1463$	$2$	(0, 1)	$-\,5851$	$1$	$76.4918296291$	$76.49182962905255$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$5851$
2.0.5867.1	$x^{2} - x + 1467$	$2$	(0, 1)	$-\,5867$	$1$	$76.5963445603$	$76.5963445602987$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$5867$
2.0.6323.1	$x^{2} - x + 1581$	$2$	(0, 1)	$-\,6323$	$1$	$79.5172937165$	$79.51729371652434$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$6323$
2.0.6691.1	$x^{2} - x + 1673$	$2$	(0, 1)	$-\,6691$	$1$	$81.7985329942$	$81.79853299418028$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$6691$
2.2.7057.1	$x^{2} - x - 1764$	$2$	(2, 0)	$7057$	$1$	$84.0059521701$	$84.00595217006948$		✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	$1$	$5.12399940836$	$2$	$7057$
2.0.7907.1	$x^{2} - x + 1977$	$2$	(0, 1)	$-\,7907$	$1$	$88.9213135306$	$88.92131353055915$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$7907$
2.0.8059.1	$x^{2} - x + 2015$	$2$	(0, 1)	$-\,8059$	$1$	$89.7719332531$	$89.77193325310535$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8059$
2.0.8123.1	$x^{2} - x + 2031$	$2$	(0, 1)	$-\,8123$	$1$	$90.1276871999$	$90.12768719988325$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8123$
2.0.8171.1	$x^{2} - x + 2043$	$2$	(0, 1)	$-\,8171$	$1$	$90.3935838431$	$90.39358384310249$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8171$
2.0.8243.1	$x^{2} - x + 2061$	$2$	(0, 1)	$-\,8243$	$1$	$90.7909687139$	$90.79096871385391$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8243$
2.0.8387.1	$x^{2} - x + 2097$	$2$	(0, 1)	$-\,8387$	$1$	$91.5805656239$	$91.58056562393574$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8387$
2.0.8627.1	$x^{2} - x + 2157$	$2$	(0, 1)	$-\,8627$	$1$	$92.8816451189$	$92.88164511893618$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8627$
2.0.8747.1	$x^{2} - x + 2187$	$2$	(0, 1)	$-\,8747$	$1$	$93.5253976201$	$93.52539762011173$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$8747$
2.0.9091.1	$x^{2} - x + 2273$	$2$	(0, 1)	$-\,9091$	$1$	$95.3467356547$	$95.34673565466203$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$9091$
2.0.9187.1	$x^{2} - x + 2297$	$2$	(0, 1)	$-\,9187$	$1$	$95.8488393253$	$95.84883932526257$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$9187$
2.0.9811.1	$x^{2} - x + 2453$	$2$	(0, 1)	$-\,9811$	$1$	$99.0504921744$	$99.05049217444606$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$9811$
2.0.9859.1	$x^{2} - x + 2465$	$2$	(0, 1)	$-\,9859$	$1$	$99.2924971989$	$99.29249719893241$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$9859$
2.0.10067.1	$x^{2} - x + 2517$	$2$	(0, 1)	$-\,10067$	$1$	$100.334440747$	$100.33444074693395$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$10067$
2.0.10771.1	$x^{2} - x + 2693$	$2$	(0, 1)	$-\,10771$	$1$	$103.78342835$	$103.78342834961659$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$10771$
2.0.11731.1	$x^{2} - x + 2933$	$2$	(0, 1)	$-\,11731$	$1$	$108.309741021$	$108.3097410208334$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$11731$
2.0.12107.1	$x^{2} - x + 3027$	$2$	(0, 1)	$-\,12107$	$1$	$110.031813581$	$110.03181358134565$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$12107$
2.0.12547.1	$x^{2} - x + 3137$	$2$	(0, 1)	$-\,12547$	$1$	$112.013392056$	$112.01339205648581$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$12547$
2.0.13171.1	$x^{2} - x + 3293$	$2$	(0, 1)	$-\,13171$	$1$	$114.764977236$	$114.76497723608888$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$13171$
2.0.13291.1	$x^{2} - x + 3323$	$2$	(0, 1)	$-\,13291$	$1$	$115.286599395$	$115.28659939472584$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$13291$
2.0.13339.1	$x^{2} - x + 3335$	$2$	(0, 1)	$-\,13339$	$1$	$115.494588618$	$115.49458861782226$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$13339$
2.0.13723.1	$x^{2} - x + 3431$	$2$	(0, 1)	$-\,13723$	$1$	$117.145209036$	$117.14520903562382$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$13723$
2.0.14419.1	$x^{2} - x + 3605$	$2$	(0, 1)	$-\,14419$	$1$	$120.07914057$	$120.07914056987583$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$14419$
2.0.14563.1	$x^{2} - x + 3641$	$2$	(0, 1)	$-\,14563$	$1$	$120.677255521$	$120.67725552066554$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$14563$
2.0.15427.1	$x^{2} - x + 3857$	$2$	(0, 1)	$-\,15427$	$1$	$124.20547492$	$124.20547491958638$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$15427$
2.0.16339.1	$x^{2} - x + 4085$	$2$	(0, 1)	$-\,16339$	$1$	$127.824097885$	$127.82409788455384$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$16339$
2.0.16987.1	$x^{2} - x + 4247$	$2$	(0, 1)	$-\,16987$	$1$	$130.334185845$	$130.3341858454642$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$16987$
2.0.17107.1	$x^{2} - x + 4277$	$2$	(0, 1)	$-\,17107$	$1$	$130.793730737$	$130.7937307366068$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$17107$
2.0.17707.1	$x^{2} - x + 4427$	$2$	(0, 1)	$-\,17707$	$1$	$133.067651967$	$133.06765196696003$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$17707$
2.0.17971.1	$x^{2} - x + 4493$	$2$	(0, 1)	$-\,17971$	$1$	$134.055958465$	$134.0559584651126$	✓	✓	✓	$C_2$ (as 2T1)	$[21]$	$[21]$	$2$	0	$1$	$0$	$17971$

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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.