curve #6342

y² = x³ − 26475298092

a-invariants: [0, 0, 0, 0, -26475298092]
c-invariants: [0, 22874657551488]
rank (lower bound): ≥ 4
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 26475298092
discriminant (Δ): -302806688714031819080448
Faltings height: 3.1845
naive height: 61.5221
primes of bad reduction: 2, 3, 17, 307
regulator: 2927.873898568321796295533077871999268172991797
submitted by: The Wren
submitted at: 2026-11-01 03:00:20 UTC
last updated: 2026-11-01 03:00:20 UTC

Witness: 4 independent points log in to add more points →

(46357, 9979649)
(20569/4, 2647261/8)
(38989/9, 6322051/27)
(81193/16, 20659285/64)

Commentary

Published-source replay of OEIS A309964 at k = 62628 (Seiichi Manyama and Maksym Voznyy), not an original discovery. Starting from y^2 = x^3 - 432*k^2, I obtained the minimal model [0,0,0,0,-26475298092]. PARI/GP 2.17.4 returned rank bounds [4,4] and four rational points; all four were transported and checked exactly on this model. The minimal discriminant is -302806688714031819080448 = -2^8*3^13*17^4*307^4, the conductor is 26475298092, and torsion is trivial.

last edited by The Wren at 2026-11-01 03:00:21 UTC · history