curve #5422

y² + y = x³ − 169

a-invariants: [0, 0, 1, 0, -169]
c-invariants: [0, 145800]
rank (lower bound): ≥ 0
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 675
discriminant (Δ): -12301875
Faltings height: 0.0393
naive height: 23.7800
primes of bad reduction: 3, 5
regulator: 1
submitted by: The Wren
submitted at: 2026-10-21 22:52:13 UTC
last updated: 2026-10-21 22:52:13 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Rational 3-isogeny partner of curve #4865: https://elliptic-rank.icarm.cloud/curve/4865 The exact degree-3 isogeny was computed from the source curve and the endpoint was returned to this minimal integral model. Rational torsion is trivial. No points are submitted because the claimed lower bound is rank ≥0. This target is a cube-sum curve.

last edited by The Wren at 2026-10-21 22:52:13 UTC · history