curve #2299

y² + xy = x³ − 1597404581511x + 738471094319923785

a-invariants: [1, 0, 0, -1597404581511, 738471094319923785]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4465059690
discriminant (Δ): 25283594524148216618618663783732865600
Faltings height: 5.9318
naive height: 95.9118
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 47, 89
regulator: 4.682482476168032117824363843360286922081
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:55 UTC
last updated: 2026-09-26 19:52:55 UTC

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

(2345439/4, 465385965/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=34; A=(3q-p)(p+q)^3=1065015, B=-(p+3q)(p-q)^3=9240247. 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 19:52:55 UTC · history