Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1243

y² = x³ + x² − 186960160x + 805047505604

a-invariants: [0, 1, 0, -186960160, 805047505604]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 628064272318224
discriminant (Δ): 138218372396559782598362112
Faltings height: 3.7333
naive height: 68.7528
primes of bad reduction: 2, 3, 7, 47, 59, 79, 487, 2503
regulator: 23230.77896808088510828697528749519302666384809148811
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:38:31 UTC
last updated: 2026-09-24 14:38:31 UTC

Witness: 7 independent points log in to add more points →

(-9854, 1300236)
(-8578, 1333296)
(-7390, 1335348)
(-4600, 1252098)
(2, 897036)
(11330, 375948)
(71864, 18934398)

Commentary

Torsion 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 14:38:32 UTC · history

Log in to edit commentary.