curve #2243

y² + xy = x³ − x² − 15001390694844x + 22309132448287419408

a-invariants: [1, -1, 0, -15001390694844, 22309132448287419408]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 62792730
discriminant (Δ): 1054883138598495754294070440557441000000
Faltings height: 6.3597
naive height: 102.6311
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 41
regulator: 2.706258404018964317156230655354574854309
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:20 UTC
last updated: 2026-09-26 19:49:20 UTC

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

(2099592, 259588764)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-24, q=41; A=(3q-p)(p+q)^3=722211, B=-(p+3q)(p-q)^3=27187875. 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 19:49:20 UTC · history