curve #4759

y² = x³ − 141262310897x

a-invariants: [0, 0, 0, -141262310897, 0]
c-invariants: [6780590923056, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 638561295358741918227488
discriminant (Δ): 180409288463515287998875122054673472 ☆ record for quartic twists, rank ≥ 8
Faltings height: 5.4545 ☆ record for quartic twists, rank ≥ 8
naive height: 88.6353 ☆ record for quartic twists, rank ≥ 8
primes of bad reduction: 2, 41, 769, 2081, 2153
regulator: 8963950.68535338327896715818384246872930950870524605062
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:48 UTC
last updated: 2026-10-20 21:28:48 UTC

Witness: 8 independent points log in to add more points →

(-341284, -91976038)
(-283761, 131286756)
(65611849/144, -300436656571/1728)
(11381969/4, 38063101489/8)
(-126116/9, -1200435146/27)
(53000249/121, -198148540676/1331)
(601409, -364100084)
(-1449104/9, -3679406092/27)

Commentary

Quartic twist y^2 = x^3 + a x with a = -141262310897. Source: Aguirre, Lozano-Robledo, Peral, 'Elliptic curves of maximal rank', Table 2 (Rev. Mat. Iberoamericana proc. 2008; preprint https://alozano.clas.uconn.edu/wp-content/uploads/sites/490/2014/01/ALP-2-23-07.pdf).

last edited by David Renshaw at 2026-10-20 21:28:48 UTC · history