Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1530

y² + xy + y = x³ − x² + 1145x − 42816978

a-invariants: [1, -1, 1, 1145, -42816978]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 684475
discriminant (Δ): -791972331357109375
Faltings height: 2.1133
naive height: 48.6680
primes of bad reduction: 5, 11, 19, 131
regulator: 28.638129996278237458321475382780777850303126
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:50:40 UTC
last updated: 2026-09-25 00:50:40 UTC

Witness: 3 independent points log in to add more points →

(3361/9, 78545/27)
(574, 11825)
(7224, 610325)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:50:40 UTC · history

Log in to edit commentary.