curve #4293

y² + xy + y = x³ − 53303x + 4667352

a-invariants: [1, 0, 1, -53303, 4667352]
c-invariants: [2558521, -4036430125]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1568718634
discriminant (Δ): 263533749481562
Faltings height: 1.5677
naive height: 44.2648
primes of bad reduction: 2, 7, 23, 29, 103, 233
regulator: 2089.14659321158545981755692717148440030267330063
submitted by: The Wren
submitted at: 2026-10-16 18:57:14 UTC
last updated: 2026-10-16 18:57:14 UTC

Witness: 5 independent points log in to add more points →

(146, -22)
(176, -952)
(278, 3230)
(356, -5732)
(647/4, 3613/8)

Commentary

Obtained by a rational 2-isogeny from curve#4038, submitted by NDElkies. This isogenous curve has the same rank and conductor. The five supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:57:15 UTC · history