curve #4798

y² = x³ − 56877643

a-invariants: [0, 0, 0, 0, -56877643]
c-invariants: [0, 49142283552]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 116462385836476164
discriminant (Δ): -1397548630037713968
Faltings height: 2.1607
naive height: 49.2360
primes of bad reduction: 2, 3, 23, 197, 12553
regulator: 155212.4128349359251780876107932461797230070669414399
submitted by: The Wren
submitted at: 2026-10-20 21:37:09 UTC
last updated: 2026-10-20 21:37:09 UTC

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

(403, 2928)
(1363, 49752)
(2707, 140640)
(1697/4, 35311/8)
(2017/4, 67569/8)
(3481/4, 196317/8)
(6337/16, 146655/64)

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^3-56877643. 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 21:37:09 UTC · history