curve #5404

y² = x³ − 26302117608

a-invariants: [0, 0, 0, 0, -26302117608]
c-invariants: [0, 22725029613312]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 50537029049971776
discriminant (Δ): -298858200767307493198848
Faltings height: 3.1834
naive height: 61.5090
primes of bad reduction: 2, 3, 13, 720527
regulator: 73638.66562022556651486064216336890056291130126828376
submitted by: The Wren
submitted at: 2026-10-21 21:34:44 UTC
last updated: 2026-10-21 21:34:44 UTC

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

(2977, 9035)
(3198, 80028)
(4602, 266760)
(5898, 422928)
(9802, 956800)
(18993, 2612493)
(76089/25, 5435937/125)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5378, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 974152504, apply the standard rational 3-isogeny to y^2 = x^3 - 27*974152504 = x^3 - 26302117608. 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 50537029049971776 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:34:44 UTC · history