curve #4737

y² = x³ − 975379

a-invariants: [0, 0, 0, 0, -975379]
c-invariants: [0, 842727456]
rank (lower bound): ≥ 6
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 102747332913228
discriminant (Δ): -410989331652912
Faltings height: 1.4830
naive height: 41.1043
primes of bad reduction: 2, 3, 975379
regulator: 25502.927708648293720993842197289510283052784642240
submitted by: The Wren
submitted at: 2026-10-20 21:27:23 UTC
last updated: 2026-10-20 21:27:23 UTC

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

(347, 6388)
(359, 6730)
(875, 25864)
(953/4, 28339/8)
(2143/9, 95554/27)
(5483/49, 223796/343)

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^3-975379. 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 21:27:24 UTC · history