curve #2403

y² + xy + y = x³ − 60368293938x + 5263227794785156

a-invariants: [1, 0, 1, -60368293938, 5263227794785156]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 100468830
discriminant (Δ): 2113030801584545266365960249000000
Faltings height: 5.1352
naive height: 86.0848
primes of bad reduction: 2, 3, 5, 7, 11, 23, 31, 61
regulator: 5.120538433988269315006511323503092490114
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:25 UTC
last updated: 2026-09-26 19:59:25 UTC

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

(-118810, 103782537)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=23; A=(3q-p)(p+q)^3=259875, B=-(p+3q)(p-q)^3=1817251. 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 19:59:26 UTC · history