Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4417

y² + xy + y = x³ − x² − 1280502x + 24610224630

a-invariants: [1, -1, 1, -1280502, 24610224630]
c-invariants: [61464081, -21262957492185]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 261505301079507297228953
discriminant (Δ): -261505301079507297228953
Faltings height: 3.1724
naive height: 61.3760
primes of bad reduction: 431, 45533, 13325298964959011
regulator: 20625873.8698012016971613945291615779730478921328412174241330
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:02 UTC
last updated: 2026-10-17 10:23:02 UTC

Witness: 11 independent points log in to add more points →

(-2442, 115982)
(-1534, 152302)
(5400, -421195)
(188, 156034)
(2761, 203842)
(961, 155296)
(-136, 157490)
(-1264, 156221)
(-3055, -136)
(4516, -335294)
(-12193/4, -95953/8)

Commentary

BASE records/rank_11.md#13 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:02 UTC · history

Log in to edit commentary.