curve #397

y² + xy + y = x³ − 414358277117226597089349992018378x + 4081054901154391944908039080891277227782032172248

a-invariants: [1, 0, 1, -414358277117226597089349992018378, 4081054901154391944908039080891277227782032172248]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 182144907061200007139583887786097410440055870331853471060570626644527405058712102210
naive height: 237.3840 ★ record for rank ≥ 22
Faltings height: 17.7892 ★ record for rank ≥ 22
discriminant (Δ): -2641855116834374132577871224152810511120637442035180975087019855118289801626482364997169495375887500
primes of bad reduction: 2, 3, 5, 13, 23, 47, 59, 79, 35908999187, 2581334746920175932683002594587378725547900138283844984775445517
regulator: 69945745464924230806620.08589970898261462937441054911543998452475834134849446756500
submitted by: Rayan Hatout
submitted at: 2026-08-28 03:42:17 UTC
last updated: 2026-08-28 03:42:17 UTC

(9274503076947449, 1017765793309057417693575)
(-24098735311383096, 266922962041722512262280)
(3613974317067245731/9, 6861713513244161050538820985/27)
(-2717543513523929074/169, 5638264841220284523827008860/2197)
(313201270955625091/9, 152271462226875736515662425/27)
(-2554696396372101, 2263391558151113586472825)
(12498234188599737, 924448753059682299142255)
(142944959157893709/16, 66886794167605689055251025/64)
(6067347257701532184, 14944997189245153100193885160)
(86198187819240749/16, 90625215213014163038626305/64)
(8805071001422649, 1056054740943757745234575)
(178308895445352639, 74828880698216953698842065)
(16209582297165114477/16, 65248556047092691645608159265/64)
(164661704649523344, 66335536795294410169235320)
(10641293066299329, 936342026114303607036715)
(11011809513660819, 923857094141504193319795)
(45902301868648647, 9043129120903788674116135)
(224872383890470636541461933257/4147654023241, -100297093729246242513045723493260363347321575/8447025082998132539)
(302899907499363053786958/8602489, -145260373834092173050262787322742596/25231100237)
(2903400641980073136033667671/28583650489, -153581527615030992781037484288046511649715/4832552037223763)
(339998771636777395164249/16900321, -136983689066439998800821872443511255/69477219631)
(1169921087079133936966968923277819/3800125011683716, 39931346288282436478231563870173159805712444148915/234259291564494472112264)

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