curve #5398

y² = x³ − 24980935599

a-invariants: [0, 0, 0, 0, -24980935599]
c-invariants: [0, 21583528357536]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 30817142884019036484
discriminant (Δ): -269588365949398531162032
Faltings height: 3.1748
naive height: 61.4059
primes of bad reduction: 2, 3, 12953, 71429
regulator: 785559.385230664822311530648144613820153390208643764659
submitted by: The Wren
submitted at: 2026-10-21 21:23:04 UTC
last updated: 2026-10-21 21:23:04 UTC

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

(2955, 28674)
(5007, 317088)
(6222, 464643)
(7572, 639657)
(7702, 657197)
(17562, 2321973)
(21774, 3209085)
(77304/25, 8463717/125)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5377, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 925219837, apply the standard rational 3-isogeny to y^2 = x^3 - 27*925219837 = x^3 - 24980935599. The eight displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [8,8] and a nonzero Neron-Tate height determinant. Same conductor 30817142884019036484 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:23:04 UTC · history