curve #566

← home · all curves · JSON ↓

y² + xy = x³ − 318298746012291971456084504678791x + 2039007571577648162642471496259106278247745190025

a-invariants

[1, 0, 0, -318298746012291971456084504678791, 2039007571577648162642471496259106278247745190025]

rank (lower bound)

≥ 22

torsion subgroup

trivial

conductor (N)

72548489985769705815993456921762610554184824373437443618738440541474198583039510

naive height

236.1352

Faltings height

17.6319

discriminant (Δ)

267819083276951112189039759823637226129772867049177566305514645490636679496703372702309155293388800

primes of bad reduction

2, 3, 5, 7, 19, 23, 31, 53, 182131, 1765417, 6543193, 30189073, 166109673803820541, 45606261430089615342978206867

regulator

1841243274807362187752382.681383047180070207988961609645593079987009159750707205338

submitted by

Jason Ma

submitted at

2026-09-04 06:31:26 UTC

later contributions

primes of bad reduction recorded · Jason Ma · 2026-09-04 06:47:34 UTC

Witness: 22 independent points log in to add more points →

(-10664684680089272164/529, -6231287048544254016940066733/12167)
(-1166693710847695003552/73441, 34964874372122808769076026350701/19902511)
(-2019837411802347726516346/99301225, -309393594256325638337036820890627447/989536707125)
(-19049601099839626, -1090693973769142696602715)
(-50647740978345752650/5329, -797785436214699320022505735075/389017)
(7056073807102628, -379969979540332494263419)
(115943268767601852278/108241, 46421718394906626818450055029629/35611289)
(-4835375097591543418/29929, 7486105372332816115673935469737/5177717)
(56249628793454753160722/10349089, -22813563027892064781294768631460767/33293019313)
(-1441072643368972676800/877969, -1315487840181887850304578523394155/822656953)
(-2187014565303775428913/114244, -40808719792356631366108491118883/38614472)
(868581289295286194/121, -468764530907521783668878189/1331)
(17865523329844562037604/22953681, -147202689241144400607987622362356479/109971085671)
(961966366831009750/121, -139437797860039573992962305/1331)
(-271168172684494, 1457840910974369272127249)
(-62937548694434479411018/3157729, -3827615282763909594883719127448587/5611284433)
(15668191773988416417506/2024929, -571853839719131707536339423104365/2881473967)
(-3341806722555548698/169, 1703476106106608371071798857/2197)
(181792255977810654345186734/32569059961, 3882173762463444324669269892175624865705/5877705682101709)
(-11674791849929375192438269804/612016759225, 517732659394691046140526092898915801976549/478789890993105875)
(-28213644431336242141258/1456849, -1704801756293398775599171760566717/1758416743)
(2583095624034358957693634/350176369, -1992366602520584349513377201142713915/6552850393097)

Commentary

No commentary yet.