curve #5393

y² + y = x³ − 595453795

a-invariants: [0, 0, 1, 0, -595453795]
c-invariants: [0, 514472078664]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 70037574653269161
discriminant (Δ): -153172175766699655107
Faltings height: 2.5521
naive height: 53.9328
primes of bad reduction: 3, 139, 634643
regulator: 158294.8875698130636943977238083030328109746091060912
submitted by: The Wren
submitted at: 2026-10-21 21:18:03 UTC
last updated: 2026-10-21 21:18:03 UTC

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

(843, 1903)
(865, 7194)
(951, 16267)
(1003, 20336)
(1201, 33717)
(3705, 224194)
(45663, 9757651)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5383, submitted by Daniel Błażewicz. Completing the square gives the Mordell model Y^2 = x^3 + 88215377/4; its standard rational 3-isogeny gives Y^2 = x^3 - 27*88215377/4, whose minimal integral model is [0,0,1,0,-595453795]. 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 70037574653269161 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:18:03 UTC · history