curve #4790

y² = x³ − 1789155

a-invariants: [0, 0, 0, 0, -1789155]
c-invariants: [0, 1545829920]
rank (lower bound): ≥ 5
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 474233424300
discriminant (Δ): -1382864665258800
Faltings height: 1.5841
naive height: 42.3177
primes of bad reduction: 2, 3, 5, 29, 457
regulator: 1633.40122267407422207040822120466879367202286893
submitted by: The Wren
submitted at: 2026-10-20 21:35:45 UTC
last updated: 2026-10-20 21:35:45 UTC

Witness: 5 independent points log in to add more points →

(151, 1286)
(219, 2952)
(471, 10134)
(631, 15794)
(1209/4, 40653/8)

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+66265, giving y^2=x^3-1789155. I recovered five rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [5,5]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:35:45 UTC · history