curve #2275

y² + xy = x³ − 3605697441410x + 2120509160979260100

a-invariants: [1, 0, 0, -3605697441410, 2120509160979260100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2323050510
discriminant (Δ): 1057669423695267085256642924875776000000
Faltings height: 6.2036
naive height: 98.3542
primes of bad reduction: 2, 3, 5, 11, 17, 29, 109, 131
regulator: 8.694471230117119049929092874226889803949
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:23 UTC
last updated: 2026-09-26 19:51:23 UTC

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

(5991535/4, 2261406245/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=40; A=(3q-p)(p+q)^3=3194959, B=-(p+3q)(p-q)^3=14458959. 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 19:51:23 UTC · history