curve #4775

y² = x³ + 26335233

a-invariants: [0, 0, 0, 0, 26335233]
c-invariants: [0, -22753641312]
rank (lower bound): ≥ 6
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 102747332913228
discriminant (Δ): -299611222774972848
Faltings height: 2.0323
naive height: 47.6960
primes of bad reduction: 2, 3, 975379
regulator: 2833.6586342942548578882046885877233647836427380267
submitted by: The Wren
submitted at: 2026-10-20 21:30:02 UTC
last updated: 2026-10-20 21:30:02 UTC

Witness: 6 independent points log in to add more points →

(-264, 2817)
(-138, 4869)
(-48, 5121)
(42, 5139)
(123, 5310)
(456, 11007)

Commentary

From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of the Mordell curve y^2=x^3-975379, giving y^2=x^3+26335233. I recovered six rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [6,6]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:30:02 UTC · history