curve #2415

y² + xy + y = x³ − 43111874858x + 3301450485412556

a-invariants: [1, 0, 1, -43111874858, 3301450485412556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 145680990
discriminant (Δ): 419641110208951190337947510250000
Faltings height: 5.0203
naive height: 85.0748
primes of bad reduction: 2, 3, 5, 7, 13, 17, 43, 73
regulator: 4.945438934105033578066365231192149332181
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:11 UTC
last updated: 2026-09-26 20:00:11 UTC

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

(77157, 20803693)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=15; A=(3q-p)(p+q)^3=-160381, B=-(p+3q)(p-q)^3=1351619. 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 20:00:11 UTC · history