curve #2604

y² + xy + y = x³ − 14820667083734x + 21956998285074716696

a-invariants: [1, 0, 1, -14820667083734, 21956998285074716696]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5192997810
discriminant (Δ): 73624888444392981043347313263293744400
Faltings height: 6.2633
naive height: 102.5947
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 67, 89
regulator: 24.2755182125999965434104675884723874329066
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:12 UTC
last updated: 2026-09-26 20:12:12 UTC

Witness: 2 independent points log in to add more points →

(8532711/4, 1758636689/8)
(2179353, 91346953)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=39; A=(3q-p)(p+q)^3=192995, B=-(p+3q)(p-q)^3=26767907. 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 20:12:12 UTC · history