Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1509

y² = x³ − x² − 987089x + 1197788865

a-invariants: [0, -1, 0, -987089, 1197788865]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 168006048
discriminant (Δ): -557896126798485393408
Faltings height: 2.6651
naive height: 55.3301
primes of bad reduction: 2, 3, 7, 29, 37, 233
regulator: 49.62000304492320611671883364852426523546907098
submitted by: hdeping
submitted at: 2026-09-25 00:43:33 UTC
last updated: 2026-09-25 00:43:33 UTC

Witness: 4 independent points log in to add more points →

(15803, 1982904)
(-1249, 21924)
(2261, 102564)
(11141, 1171716)

Commentary

Specialization t=1073/392 of the Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2.

last edited by hdeping at 2026-09-27 08:26:16 UTC · history

Log in to edit commentary.