curve #4809

y² = x³ − 2520963512

a-invariants: [0, 0, 0, 0, -2520963512]
c-invariants: [0, 2178112474368]
rank (lower bound): ≥ 8
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 57197313259518367296
discriminant (Δ): -2745471036456881630208
Faltings height: 2.7926
naive height: 56.8190
primes of bad reduction: 2, 3, 311, 1013249
regulator: 902205.665137568961284890186175520908920124522039126087
submitted by: The Wren
submitted at: 2026-10-20 21:41:46 UTC
last updated: 2026-10-20 21:41:46 UTC

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

(1361, 213)
(1662, 45496)
(2126, 84192)
(2802, 139564)
(5961, 457487)
(7433, 638865)
(10737, 1111429)
(7673/4, 538893/8)

Commentary

From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. The Mordell curve y^2=x^3-2520963512. 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 21:41:46 UTC · history