curve #4811

y² = x³ − 44069440419

a-invariants: [0, 0, 0, 0, -44069440419]
c-invariants: [0, 38075996522016]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 95906942165125476324
discriminant (Δ): -838993930060517666882352
Faltings height: 3.2694
naive height: 62.5412
primes of bad reduction: 2, 3, 10891, 149867
regulator: 2944491.57668075950044024104120895648903503972523219651
submitted by: The Wren
submitted at: 2026-10-20 21:43:55 UTC
last updated: 2026-10-20 21:43:55 UTC

Witness: 8 independent points log in to add more points →

(3867, 117288)
(8695, 783134)
(9739, 937900)
(16633/4, 1334611/8)
(17305/4, 1536803/8)
(17881/4, 1701955/8)
(32755/9, 1736632/27)
(74625/4, 20316447/8)

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+1632201497, giving y^2=x^3-44069440419. I recovered eight rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [8,8]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:43:56 UTC · history