Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4337

y² = x³ + x² − 34563861x + 297542599300

a-invariants: [0, 1, 0, -34563861, 297542599300]
c-invariants: [1659065344, -257086760187232]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 31146261647020
discriminant (Δ): -35605919287133726924252080
Faltings height: 3.5858
naive height: 66.3609
primes of bad reduction: 2, 5, 13, 17, 41, 59, 223, 13063
regulator: 1763.8282505896928968195938467401804905575726850558
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:22 UTC
last updated: 2026-10-17 10:05:22 UTC

Witness: 6 independent points log in to add more points →

(-7329, 396539)
(1069539, -1106085331)
(78575, 21970715)
(-59825/9, 13050505/27)
(16389, -2033081)
(126129, 44749081)

Commentary

BASE torsion/torsion_Z3.tsv.gz:491 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:22 UTC · history

Log in to edit commentary.