Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1687

y² + xy = x³ + x² − 27932649625x + 3199186402575625

a-invariants: [1, 1, 0, -27932649625, 3199186402575625]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 9680213412150 ☆ record for ℤ/4ℤ torsion, rank ≥ 6
discriminant (Δ): -3026648772882909341988797590312500
Faltings height: 5.1177
naive height: 84.9265
primes of bad reduction: 2, 3, 5, 41, 61, 101, 449, 569
regulator: 10086.022056395613373688268633127829018604760097631
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:08 UTC
last updated: 2026-09-25 06:10:08 UTC

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

(1388655, 1624803535)
(11161921/121, 49872754106/1331)
(26145211/49, 128341728493/343)
(121569600/289, -1262106718675/4913)
(403100, 239463425)
(773650/9, 1021019575/27)

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 06:10:08 UTC · history

Log in to edit commentary.