curve #3951

y² + xy + y = x³ + x² − 120530476346973725813x + 509244197373943797663174128906

a-invariants: [1, 1, 1, -120530476346973725813, 509244197373943797663174128906]
c-invariants: [5785462864654738839025, -439986986574478412665892988667625]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 7107840925923552917025
discriminant (Δ): 34744205120513052145261024329829466913014705809192578515625
Faltings height: 10.2370
naive height: 150.3289
primes of bad reduction: 3, 5, 7, 11, 19, 101, 239, 251, 311, 5519, 6229
regulator: 24141627434.1507353065433175808196185804987206333631944
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:32:58 UTC
last updated: 2026-10-05 04:32:58 UTC

Witness: 8 independent points log in to add more points →

(329367683411641/81, -5977505773271651142745/729)
(994867752141/25, -957966032517812851/125)
(556295686938050661/86638864, -5734043841721732953519631/806434546112)
(12217539831021/1849, -2886518137421240501/79507)
(195172207030341/29584, 177058867369767283849/5088448)
(387061648769655531/60310756, -3001397447438889490253965/468373331096)
(4505398569814628716634125/685680462621001, -555970402445902756864426481877241063/17954886439642684306501)
(4449715924110496165161/693487552081, 3508412279136878420122403496037/577508000383421479)

Commentary

Unlisted rational-isogeny neighbor of curve#3669 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:32:59 UTC · history