curve #2444

y² + xy = x³ − 11498154956x − 59287297895280

a-invariants: [1, 0, 0, -11498154956, -59287297895280]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 50907270
discriminant (Δ): 95770734286110045127440151449600
Faltings height: 4.8264
naive height: 81.1100
primes of bad reduction: 2, 3, 5, 19, 31, 43, 67
regulator: 7.695519267742468112617454972788586841466
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:59 UTC
last updated: 2026-09-26 20:01:59 UTC

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

(475774, 319397650)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=12; A=(3q-p)(p+q)^3=-459553, B=-(p+3q)(p-q)^3=397535. 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 20:01:59 UTC · history