curve #4805

y² = x³ + 1535696361

a-invariants: [0, 0, 0, 0, 1535696361]
c-invariants: [0, -1326841655904]
rank (lower bound): ≥ 7
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 116462385836476164
discriminant (Δ): -1018812951297493482672
Faltings height: 2.7100
naive height: 55.8276
primes of bad reduction: 2, 3, 23, 197, 12553
regulator: 51737.47094497864172602920359774872657433568898047998
submitted by: The Wren
submitted at: 2026-10-20 21:38:49 UTC
last updated: 2026-10-20 21:38:49 UTC

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

(-1146, 5535)
(-1010, 22481)
(150, 39231)
(852, 46413)
(1122, 54297)
(3390, 201231)
(8007, 717552)

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^3-56877643, giving y^2=x^3+1535696361. 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 21:38:49 UTC · history