curve #2338

y² + xy + y = x³ − 419414718749x + 85028848077118916

a-invariants: [1, 0, 1, -419414718749, 85028848077118916]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 369244590
discriminant (Δ): 1598515307095866683721660829797502500
Faltings height: 5.6635
naive height: 91.9000
primes of bad reduction: 2, 3, 5, 11, 13, 17, 61, 83
regulator: 4.238856210815355827190708687651325587645
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:55:21 UTC
last updated: 2026-09-26 19:55:21 UTC

Witness: 1 independent point log in to add more points →

(-553002, 384791638)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-50, q=11; A=(3q-p)(p+q)^3=-4923477, B=-(p+3q)(p-q)^3=-3858677. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:55:21 UTC · history