Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #2045

y² + xy + y = x³ − 803641707349x + 713758883634340206

a-invariants: [1, 0, 1, -803641707349, 713758883634340206]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 6647665425830
discriminant (Δ): -186865661555244231666759662152972126870
Faltings height: 6.0300
naive height: 95.7418
primes of bad reduction: 2, 5, 11, 13, 29, 173, 193, 4801
regulator: 37296.6592494100679552720019283991359444223180677
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:08:02 UTC
last updated: 2026-09-26 05:08:02 UTC

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

(-53418300/49, -185867038734/343)
(-4080398634/3481, 43761105535363/205379)
(-1009007376/2809, 145597960313169/148877)
(522002886546/124609, 370186462717849636/43986977)
(181506700299817246/594279101025, -322975879556997239962143841/458126787584667375)

Commentary

2-isogenous partner of curve#1248 (hdeping).

last edited by Steps Unbounded at 2026-09-26 21:50:55 UTC · history

Log in to edit commentary.