curve #5400

y² + y = x³ − 265578865

a-invariants: [0, 0, 1, 0, -265578865]
c-invariants: [0, 229460139144]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 13932273264572601
discriminant (Δ): -30469881629620278387
Faltings height: 2.4175
naive height: 52.3180
primes of bad reduction: 3, 39345017
regulator: 107724.7562713901639160537107620518160467425546266283
submitted by: The Wren
submitted at: 2026-10-21 21:25:00 UTC
last updated: 2026-10-21 21:25:00 UTC

Witness: 7 independent points log in to add more points →

(643, 518)
(645, 1660)
(691, 8022)
(753, 12703)
(2103, 95053)
(9663, 949738)
(35349/25, 6326132/125)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5375, submitted by Daniel Błażewicz. Completing the square gives the Mordell model Y^2 = x^3 + 39345017/4; applying the standard rational 3-isogeny and returning to a minimal integral model gives [0,0,1,0,-265578865]. The seven displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [7,7] and a nonzero Neron-Tate height determinant. Same conductor 13932273264572601 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:25:00 UTC · history