curve #4717

y² = x³ + 1358556

a-invariants: [0, 0, 0, 0, 1358556]
c-invariants: [0, -1173792384]
rank (lower bound): ≥ 6
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 49833208938672
discriminant (Δ): -797331343018752
Faltings height: 1.5382
naive height: 41.7670
primes of bad reduction: 2, 3, 113213
regulator: 5949.3459158112009516773871142764891323717318315581
submitted by: The Wren
submitted at: 2026-10-20 21:25:41 UTC
last updated: 2026-10-20 21:25:41 UTC

Witness: 6 independent points log in to add more points →

(-110, 166)
(-86, 850)
(-11, 1165)
(10, 1166)
(82, 1382)
(-47/4, 9319/8)

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+1358556. I recovered six rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [6,6]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:25:41 UTC · history