curve #498

y² + xy = x³ − x² − 15297408947381357398079937033609099x + 762501772320862356783982575679345414430261434414793

a-invariants: [1, -1, 0, -15297408947381357398079937033609099, 762501772320862356783982575679345414430261434414793]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 1680504780621606551270041139722019335716435894937324741135209754088510728125973074570
discriminant (Δ): -22064175471158729845659514423468373748899509403319010957867968656809418997389145405637293493345597312500
Faltings height: 18.5874
naive height: 247.8445
primes of bad reduction: 2, 3, 5, 11, 13, 109, 569, 248867, 135399998003273, 62479345364602812587306193715261274044903241967815444401
regulator: 369346081762487442677288.784108818986113777419271599112307882035676320694710022800728
submitted by: Rayan Hatout
submitted at: 2026-09-02 10:32:27 UTC
last updated: 2026-09-02 10:32:27 UTC

(96422583145652452, 13563081109463651721729589)
(-44258964265677661, 36781140763137345524441170)
(14879329443205524949/121, 36228515254611274797371639771/1331)
(156258925836449929798/2209, 608558719018934438858382639557/103823)
(3990285674843176475323/529, 252027528187360394805294902663678/12167)
(10684826692412255092/81, 23508870467649264447990121261/729)
(2201631104828739011062/32041, 34315253576294248556723883506501/5735339)
(2775636387785401862, 4619766438024851157711863979)
(-2951960466069647888/1681, 1936373168468393431283363979419/68921)
(3763649129430674373238/32041, 138877956518567221765164038025209/5735339)
(-773599073899077253847/5929, 10581164334905455924493277423497/456533)
(158430109441347813493/1849, 714813201556209704489446021438/79507)
(291756267927124249, 145376002478616654666279085)
(48557344383829656427/361, 231428595211662185095090924681/6859)
(3182109140768361382, -5672172808380405892512642341)
(3682012176288764182, 7061321620332140998677860659)
(189208866859551832, -68130557874969610041037091)
(16525112441229483148/49, -63209352461116159841720255063/343)
(5104664219926536355417/1681, -364414936113518769362943518530411/68921)
(640040005327653652, 503154756874665394725438709)
(181680822713484772, -63088527057516812122975691)
(591942345800802652, 446230203046177649194262389)
(428299418964605728363/5041, -3122505724476539937860509339234/357911)

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