Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4536

y² + y = x³ − x² − 405879532526410x + 3177550882352575277602

a-invariants: [0, -1, 1, -405879532526410, 3177550882352575277602]
c-invariants: [19482217561267696, -2745403845459319672242200]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 2831065189961723
discriminant (Δ): -82542881183348809079303503884813387831334763
Faltings height: 7.2415
naive height: 112.5439
primes of bad reduction: 11, 13, 19, 23, 29, 137, 11402861
regulator: 4226.09675661448688650017789277120701883346082659
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:25 UTC
last updated: 2026-10-17 10:34:25 UTC

Witness: 5 independent points log in to add more points →

(-19550497, 60332978790)
(-1347280190/81, -53206396073783/729)
(6054589, 30693101939)
(17956342945/1849, -979548594684643/79507)
(399137185/64, 15264469155537/512)

Commentary

BASE torsion/torsion_Z5.tsv.gz:1322 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:25 UTC · history

Log in to edit commentary.