curve #6338

y² + y = x³ − 9075165001

a-invariants: [0, 0, 1, 0, -9075165001]
c-invariants: [0, 7840942560648]
rank (lower bound): ≥ 4
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 36300660003
discriminant (Δ): -35578923749641906920243
Faltings height: 3.0061
naive height: 59.3808
primes of bad reduction: 3, 37, 991
regulator: 254.3589151102224944951405820947006842544230821
submitted by: The Wren
submitted at: 2026-11-01 02:39:45 UTC
last updated: 2026-11-01 02:39:45 UTC

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

(14097/4, 1490171/8)
(110001/16, 35970295/64)
(110001/25, 34485251/125)
(476671/25, 328884594/125)

Commentary

Published-source replay from OEIS A309964: k=36667 in the rank-4 sequence for y² = x³ − 432k². The global minimal model is [0,0,1,0,−9075165001]. PARI/GP 2.17.4 returned exact rank bounds [4,4] with trivial torsion. All four displayed points were checked on this model. The discriminant factors as −3^9·37^4·991^4 and the conductor is 36300660003. Here c4=0 and 2c6=3960036², so ICARM classifies the curve as cube-sum. This is a published construction replay, not an original discovery.

last edited by The Wren at 2026-11-01 02:39:45 UTC · history