Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4519

y² = x³ + x² − 69574732158x + 7329867249804913

a-invariants: [0, 1, 0, -69574732158, 7329867249804913]
c-invariants: [3339587143600, -6333025341354306400]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 265300607396278300
discriminant (Δ): -1655857204259630955951681768070000
Faltings height: 5.1389
naive height: 86.5846
primes of bad reduction: 2, 5, 7, 11, 37, 47, 59, 1361, 246739
regulator: 11288.29830708835002545854478424181846650731674964792
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:26 UTC
last updated: 2026-10-17 10:33:26 UTC

Witness: 7 independent points log in to add more points →

(171813, 21164185)
(-210212, 112544565)
(-746979/4, 940132963/8)
(-26322, 95618915)
(-287883/4, 875056105/8)
(-577742/9, 2899401659/27)
(72693, 51540335)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4846 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:26 UTC · history

Log in to edit commentary.