curve #4808

y² = x³ − 1283858559

a-invariants: [0, 0, 0, 0, -1283858559]
c-invariants: [0, 1109253794976]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 244191525854452812
discriminant (Δ): -712062489391584399792
Faltings height: 2.6801
naive height: 55.4694
primes of bad reduction: 2, 3, 317, 150001
regulator: 60375.57000503329925030095231820314161748581644047681
submitted by: The Wren
submitted at: 2026-10-20 21:40:29 UTC
last updated: 2026-10-20 21:40:29 UTC

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

(1230, 24021)
(1410, 38979)
(1482, 44397)
(1500, 45729)
(2220, 98271)
(2472, 117567)
(6450, 516771)

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+47550317, giving y^2=x^3-1283858559. I recovered seven rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [7,7]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:40:29 UTC · history