Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (222541 objects)

Results (1-50 of 41166 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 $p$
2.0.71.1	$x^{2} - x + 18$	$2$	(0, 1)	$-\,71$	$1$	$8.42614977318$	$8.426149773176359$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$71$
2.0.151.1	$x^{2} - x + 38$	$2$	(0, 1)	$-\,151$	$1$	$12.2882057274$	$12.288205727444508$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$151$
2.0.223.1	$x^{2} - x + 56$	$2$	(0, 1)	$-\,223$	$1$	$14.9331845231$	$14.933184523068078$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$223$
2.0.251.1	$x^{2} - x + 63$	$2$	(0, 1)	$-\,251$	$1$	$15.8429795178$	$15.84297951775486$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$251$
2.0.463.1	$x^{2} - x + 116$	$2$	(0, 1)	$-\,463$	$1$	$21.5174347914$	$21.517434791350013$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$463$
2.0.467.1	$x^{2} - x + 117$	$2$	(0, 1)	$-\,467$	$1$	$21.610182785$	$21.61018278497431$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$467$
2.0.487.1	$x^{2} - x + 122$	$2$	(0, 1)	$-\,487$	$1$	$22.0680764907$	$22.06807649071391$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$487$
2.2.577.1	$x^{2} - x - 144$	$2$	(2, 0)	$577$	$1$	$24.0208242989$	$24.020824298928627$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$3.87163475639$	$2$	$577$
2.0.587.1	$x^{2} - x + 147$	$2$	(0, 1)	$-\,587$	$1$	$24.2280828792$	$24.228082879171435$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$587$
2.0.811.1	$x^{2} - x + 203$	$2$	(0, 1)	$-\,811$	$1$	$28.4780617318$	$28.478061731796284$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$811$
2.0.827.1	$x^{2} - x + 207$	$2$	(0, 1)	$-\,827$	$1$	$28.7576076891$	$28.75760768909681$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$827$
2.0.859.1	$x^{2} - x + 215$	$2$	(0, 1)	$-\,859$	$1$	$29.3087017795$	$29.30870177950569$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$859$
2.2.1009.1	$x^{2} - x - 252$	$2$	(2, 0)	$1009$	$1$	$31.7647603485$	$31.76476034853718$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$6.98471717746$	$2$	$1009$
2.0.1163.1	$x^{2} - x + 291$	$2$	(0, 1)	$-\,1163$	$1$	$34.10278581$	$34.10278580995987$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1163$
2.0.1171.1	$x^{2} - x + 293$	$2$	(0, 1)	$-\,1171$	$1$	$34.2198772645$	$34.219877264537345$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1171$
2.0.1483.1	$x^{2} - x + 371$	$2$	(0, 1)	$-\,1483$	$1$	$38.5097390279$	$38.50973902793941$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1483$
2.0.1523.1	$x^{2} - x + 381$	$2$	(0, 1)	$-\,1523$	$1$	$39.0256326022$	$39.02563260217571$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1523$
2.2.1601.1	$x^{2} - x - 400$	$2$	(2, 0)	$1601$	$1$	$40.0124980475$	$40.01249804748511$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$4.38218284807$	$2$	$1601$
2.0.1627.1	$x^{2} - x + 407$	$2$	(0, 1)	$-\,1627$	$1$	$40.3360880602$	$40.33608806019741$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1627$
2.2.1761.1	$x^{2} - x - 440$	$2$	(2, 0)	$3\cdot 587$	$2$	$41.9642705167$	$41.96427051671457$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$7.76217042606$	$1$	$587$
2.0.1787.1	$x^{2} - x + 447$	$2$	(0, 1)	$-\,1787$	$1$	$42.2729227757$	$42.2729227756965$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1787$
2.0.1987.1	$x^{2} - x + 497$	$2$	(0, 1)	$-\,1987$	$1$	$44.575778176$	$44.57577817604534$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$1987$
2.0.2011.1	$x^{2} - x + 503$	$2$	(0, 1)	$-\,2011$	$1$	$44.8441746496$	$44.844174649557324$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2011$
2.2.2029.1	$x^{2} - x - 507$	$2$	(2, 0)	$2029$	$1$	$45.0444225182$	$45.044422518220834$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$3.80715595153$	$2$	$2029$
2.0.2083.1	$x^{2} - x + 521$	$2$	(0, 1)	$-\,2083$	$1$	$45.639894829$	$45.639894828976104$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2083$
2.0.2179.1	$x^{2} - x + 545$	$2$	(0, 1)	$-\,2179$	$1$	$46.6797600679$	$46.67976006793523$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2179$
2.0.2251.1	$x^{2} - x + 563$	$2$	(0, 1)	$-\,2251$	$1$	$47.4447046571$	$47.44470465710583$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2251$
2.0.2467.1	$x^{2} - x + 617$	$2$	(0, 1)	$-\,2467$	$1$	$49.6689037528$	$49.66890375275057$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2467$
2.0.2707.1	$x^{2} - x + 677$	$2$	(0, 1)	$-\,2707$	$1$	$52.0288381573$	$52.028838157314254$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$2707$
2.2.2913.1	$x^{2} - x - 728$	$2$	(2, 0)	$3\cdot 971$	$2$	$53.9722150741$	$53.97221507405454$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$8.26513556372$	$1$	$971$
2.0.3019.1	$x^{2} - x + 755$	$2$	(0, 1)	$-\,3019$	$1$	$54.9454274713$	$54.945427471264615$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$3019$
2.0.3067.1	$x^{2} - x + 767$	$2$	(0, 1)	$-\,3067$	$1$	$55.380501984$	$55.380501984001555$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$3067$
2.0.3187.1	$x^{2} - x + 797$	$2$	(0, 1)	$-\,3187$	$1$	$56.4535207051$	$56.45352070508977$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$3187$
2.0.3907.1	$x^{2} - x + 977$	$2$	(0, 1)	$-\,3907$	$1$	$62.505999712$	$62.505999712027645$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$3907$
2.2.4229.1	$x^{2} - x - 1057$	$2$	(2, 0)	$4229$	$1$	$65.0307619516$	$65.03076195155643$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$4.1746238723$	$2$	$4229$
2.2.4348.1	$x^{2} - 1087$	$2$	(2, 0)	$2^{2}\cdot 1087$	$2$	$65.9393660873$	$65.93936608733814$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$7.68524339678$	$1$	$1087$
2.0.4603.1	$x^{2} - x + 1151$	$2$	(0, 1)	$-\,4603$	$1$	$67.8454125199$	$67.84541251993387$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$4603$
2.0.5107.1	$x^{2} - x + 1277$	$2$	(0, 1)	$-\,5107$	$1$	$71.4632772828$	$71.46327728281149$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$5107$
2.2.5176.1	$x^{2} - 1294$	$2$	(2, 0)	$2^{3}\cdot 647$	$2$	$71.9444229944$	$71.9444229944198$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$7.85941300562$	$1$	$647$
2.2.5273.1	$x^{2} - x - 1318$	$2$	(2, 0)	$5273$	$1$	$72.6154253585$	$72.61542535852834$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$7.54327362725$	$2$	$5273$
2.2.5417.1	$x^{2} - x - 1354$	$2$	(2, 0)	$5417$	$1$	$73.6002717386$	$73.60027173862879$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$6.60123196478$	$2$	$5417$
2.0.5923.1	$x^{2} - x + 1481$	$2$	(0, 1)	$-\,5923$	$1$	$76.9610290991$	$76.96102909914862$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	0	$1$	$0$	$5923$
2.2.7736.1	$x^{2} - 1934$	$2$	(2, 0)	$2^{3}\cdot 967$	$2$	$87.9545337092$	$87.95453370918409$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$8.26100971925$	$1$	$967$
2.2.8097.1	$x^{2} - x - 2024$	$2$	(2, 0)	$3\cdot 2699$	$2$	$89.9833317898$	$89.9833317898376$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$9.2871162022$	$1$	$2699$
2.2.8661.1	$x^{2} - x - 2165$	$2$	(2, 0)	$3\cdot 2887$	$2$	$93.0644937664$	$93.06449376641986$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$7.9672800588$	$1$	$2887$
2.2.8773.1	$x^{2} - x - 2193$	$2$	(2, 0)	$31\cdot 283$	$2$	$93.6642941574$	$93.66429415737889$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$5.63834200461$	$1$	$283$
2.2.9004.1	$x^{2} - 2251$	$2$	(2, 0)	$2^{2}\cdot 2251$	$2$	$94.8894093142$	$94.88940931421166$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$12.8067206916$	$1$	$2251$
2.2.9029.1	$x^{2} - x - 2257$	$2$	(2, 0)	$9029$	$1$	$95.0210502994$	$95.02105029939419$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$4.55398767651$	$2$	$9029$
2.2.9049.1	$x^{2} - x - 2262$	$2$	(2, 0)	$9049$	$1$	$95.1262319237$	$95.12623192369179$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[7]$	$2$	$1$	$21.5062273665$	$2$	$9049$
2.2.9101.1	$x^{2} - x - 2275$	$2$	(2, 0)	$19\cdot 479$	$2$	$95.3991614219$	$95.39916142189091$		✓	✓	$C_2$ (as 2T1)	$[7]$	$[14]$	$2$	$1$	$6.16751209582$	$1$	$479$

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