curve #3722

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y² + y = x³ + x² − 1366954638717973452722911319027670708x + 609863887492729249417909746749250792660527837221615844

a-invariants: [0, 1, 1, -1366954638717973452722911319027670708, 609863887492729249417909746749250792660527837221615844]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 38467542084465635972762693684906185313856707044550710834592470682480424596308234522769175641925
discriminant (Δ): 2796117407666665291359052361628855073660145036990701041259730140978000980480979292169135723391741290274183125 ★ record for rank ≥ 25
Faltings height: 19.6278 ★ record for rank ≥ 25
naive height: 261.2305 ★ record for rank ≥ 25
primes of bad reduction: 3, 5, 7, 11, 17, 47, 766877, 12775211305623734495189, 850945732792224912158102382590358479169996453815232822957461
regulator: 28316092481615037487414591677297.82737550191380068730765036437037842692971119440694361108
submitted by: Matej Jurasić
submitted at: 2026-09-30 20:01:06 UTC
last updated: 2026-09-30 20:01:06 UTC

Witness: 25 independent points log in to add more points →

(622659767820200013, 11164717323240682912071322)
(3573118591167856788, 6429946224032880434535635947)
(1043161039911976203, -564855923690282049948301253)
(1584553786589543673, 1556394983551057440587180422)
(1816356574892741169, 2029635885709674450001938721)
(1794511585002166797/4, 2358357253974850959173480441/8)
(1298907896174441904, -1012809655041625759026244757)
(612131564589526038, -49765407024240563522755928)
(2078758368255413748, 2598288229675622385016701547)
(849243046973322324, -247937350974243065554854677)
(8411676340638568713/16, -12230956216594468492036763597/64)
(725740434281045072, -7518276948864056985757676)
(-248108526857248143, 966304281225160517637873694)
(8575552047429815513/16, -11301211039427005026777300347/64)
(-123550181697927888, -881399700203961421743785621)
(24676681535859393993, -122447793583567162804897249898)
(47134500762468544857/64, 26092168771995732402361402499/512)
(383952700861855852956276045237/2037800164, -237907563188197448653391741957859191396224349/91990375003288)
(5836512127191752793925864527/8044116721, 3123132706422220932656153953225348509151/721468784589769)
(14497097970321383669557475707128/5399911660441, 50645637793949376748236440958214572259447051297/12548158119094643011)
(759499512512994182774306619322491/1460272575801169, -11103848391520024368604207154691074339404734664573/55802145058921456996697)
(57934831275714478666314207738387/690060361, -440970583929957097060778832629972875520415680060/18127195623109)
(2801826397661511507011655619812582/1494198433548769, -124412958051904538810586517519097932017808097813831/57758035743642269513647)
(602246285090727553453423874896983/3636157010641, 14779182195260521546159883754469334453822638665017/6933682355038014311)
(70742876008974945506289445303383/2735560526209, 594411820132374128890554209237072766379213402640/4524488539004954177)

Commentary

Specialization at T = -173/65 of a rank-17 fibration of X1092 (2-neighbour of the one in curve#1879).

last edited by Matej Jurasić at 2026-09-30 20:01:06 UTC · history