Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1704

y² + xy + y = x³ + x² − 426346764475x + 321489090726259370

a-invariants: [1, 1, 1, -426346764475, 321489090726259370]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 91043416225155
discriminant (Δ): -39689657108372826432432440057491128585
Faltings height: 5.8992
naive height: 94.1466
primes of bad reduction: 3, 5, 29, 53, 149, 709, 1289
regulator: 78896.760693983195508433045528621658581047612362808
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:12:58 UTC
last updated: 2026-09-25 06:12:58 UTC

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

(3136004, 5459711490)
(-856600, 241585470)
(-1003705295/9216, 535755872938489/884736)
(41637950/49, 259447085547/343)
(-615965, 592253245)
(1475870, -1705727091)

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 06:12:58 UTC · history

Log in to edit commentary.