curve #4845

y² = x³ + 15

a-invariants: [0, 0, 0, 0, 15]
c-invariants: [0, -12960]
rank (lower bound): ≥ 2
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 97200
discriminant (Δ): -97200
Faltings height: -0.3641
naive height: 18.9392
primes of bad reduction: 2, 3, 5
regulator: 3.76262022543869176040092676587236791400378
submitted by: The Wren
submitted at: 2026-10-20 22:04:31 UTC
last updated: 2026-10-20 22:04:31 UTC

Witness: 2 independent points log in to add more points →

(1, 4)
(1/4, 31/8)

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+15. I recovered two rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [2,2]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 22:04:31 UTC · history