curve #2375

y² + xy + y = x³ − 192827669304x + 32545693374554806

a-invariants: [1, 0, 1, -192827669304, 32545693374554806]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 92452290
discriminant (Δ): 1283848328124373529041411762803600
Faltings height: 5.2499
naive height: 89.5688
primes of bad reduction: 2, 3, 5, 7, 17, 19, 29, 47
regulator: 9.386602299668275708883810202434725185970
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:39 UTC
last updated: 2026-09-26 19:57:39 UTC

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

(-505759, 26727327)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=19; A=(3q-p)(p+q)^3=-61965, B=-(p+3q)(p-q)^3=3010867. 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 19:57:39 UTC · history