Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1300

y² = x³ + x² − 706785x + 1586454079

a-invariants: [0, 1, 0, -706785, 1586454079]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 73879116224
discriminant (Δ): -1064999768593034149888
Faltings height: 2.7153
naive height: 55.8930
primes of bad reduction: 2, 23, 41, 73, 409
regulator: 302.37721183355163537959023364507987274104888752246
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:28:13 UTC
last updated: 2026-09-24 17:28:13 UTC

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

(-53, 40296)
(1626, 68839)
(683, 37720)
(4619, 311272)
(3305, 188048)
(-28189/25, 3854984/125)

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 17:28:13 UTC · history

Log in to edit commentary.