Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1310

y² = x³ − x² − 2038949201x + 34895482334001

a-invariants: [0, -1, 0, -2038949201, 34895482334001]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 21392949126720
discriminant (Δ): 16475697804183480382246502400
Faltings height: 4.2107
naive height: 75.9207
primes of bad reduction: 2, 3, 5, 17, 19, 31, 59, 67, 563
regulator: 1368.2618849891726027364914879503382354377665839891
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:55 UTC
last updated: 2026-09-24 17:29:55 UTC

Witness: 6 independent points log in to add more points →

(-11515, 7539696)
(1210195, 1330407284)
(-136699/121, 8117739360/1331)
(33525, 2053824)
(-424611/49, 2471344800/343)
(30893, 1178496)

Commentary

Torsion Z/2+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:29:55 UTC · history

Log in to edit commentary.