curve #4760

y² = x³ − 727465200962x

a-invariants: [0, 0, 0, -727465200962, 0]
c-invariants: [34918329646176, 0]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 33869159591083714926428416
discriminant (Δ): 24638634988341764422319766690347336192
Faltings height: 5.8642
naive height: 93.5521
primes of bad reduction: 2, 41, 1601, 2137, 2593
regulator: 69256283.355129289365383471228879942511111174000552893354
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:53 UTC
last updated: 2026-10-20 21:28:53 UTC

Witness: 9 independent points log in to add more points →

(3421337/4, 475565843/8)
(1577106, -1665949638)
(5316921/4, -9403270173/8)
(-627592, -457559396)
(-30792033/49, -156803296047/343)
(2334258, -3319747146)
(14373778/9, -46073107306/27)
(-706041, -402073539)
(-2053657/529, -646578470899/12167)

Commentary

Quartic twist y^2 = x^3 + a x with a = -727465200962. 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 21:28:53 UTC · history