Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1468

y² + xy = x³ + 135956646x + 128109873780

a-invariants: [1, 0, 0, 135956646, 128109873780]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/8ℤ
conductor (N): 1805874
discriminant (Δ): -167924063267784813159022608
Faltings height: 3.7214
naive height: 67.7971
primes of bad reduction: 2, 3, 7, 19, 31, 73
regulator: 31.9314083152302374827778544902573247844865
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:12:19 UTC
last updated: 2026-09-25 00:12:19 UTC

Witness: 2 independent points log in to add more points →

(-101514/121, 154963158/1331)
(316596, -178418142)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:12:19 UTC · history

Log in to edit commentary.