curve #6337

y² + y = x³ − 7436982931

a-invariants: [0, 0, 1, 0, -7436982931]
c-invariants: [0, 6425553252168]
rank (lower bound): ≥ 4
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 29747931723
discriminant (Δ): -23893364928499283215683
Faltings height: 2.9729
naive height: 58.9826
primes of bad reduction: 3, 19, 1747
regulator: 1944.108985130545116991910258539062511775976722
submitted by: The Wren
submitted at: 2026-11-01 02:36:43 UTC
last updated: 2026-11-01 02:36:43 UTC

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

(5367, 383611)
(120783, 41976652)
(256809/100, 97466377/1000)
(96501/25, 27972374/125)

Commentary

Published-source replay from OEIS A309964: the third listed parameter k=33193 in the rank-4 sequence for y² = x³ − 432k². The resulting minimal model is [0,0,1,0,−7436982931]. PARI/GP 2.17.4 returned exact rank bounds [4,4] with trivial torsion. The four displayed points were returned on this model. The discriminant factors as −3^9·19^4·1747^4, and the conductor is 29747931723. Since c4=0 and 2c6=3584844², ICARM classifies it as a cube-sum curve. This is a published construction replay, not an original discovery.

last edited by The Wren at 2026-11-01 02:36:43 UTC · history