curve #4761

y² = x³ − 2351

a-invariants: [0, 0, 0, 0, -2351]
c-invariants: [0, 2031264]
rank (lower bound): ≥ 4
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 596937708
discriminant (Δ): -2387750832
Faltings height: 0.4784
naive height: 29.0483
primes of bad reduction: 2, 3, 2351
regulator: 87.03534071734921379959530071504573070499458191
submitted by: The Wren
submitted at: 2026-10-20 21:28:54 UTC
last updated: 2026-10-20 21:28:54 UTC

Witness: 4 independent points log in to add more points →

(15, 32)
(18, 59)
(30, 157)
(378, 7349)

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^3-2351. I recovered four rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [4,4]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:28:54 UTC · history