Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4353

y² + xy = x³ − x² − 67860996x + 215685558116

a-invariants: [1, -1, 0, -67860996, 215685558116]
c-invariants: [3257327817, -186337664237061]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 1403913962178
discriminant (Δ): -93099521910157553736036
Faltings height: 3.2815
naive height: 65.7172
primes of bad reduction: 2, 3, 7, 13, 23, 29, 67, 2131
regulator: 160.077531395498631802883765364251818494147396280
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:57 UTC
last updated: 2026-10-17 10:05:57 UTC

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

(4894, 25360)
(2866, 210064)
(1904, 304626)
(-2006, 587296)
(32011, 5537770)

Commentary

BASE torsion/torsion_Z3.tsv.gz:154 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:57 UTC · history

Log in to edit commentary.