curve #2616

y² + xy = x³ − 1293523450555x + 204817827102067025

a-invariants: [1, 0, 0, -1293523450555, 204817827102067025]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 838767930
discriminant (Δ): 120394374546008210967569390765625000000
Faltings height: 5.9997
naive height: 95.2788
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 31, 53
regulator: 16.4235684714226264964438624612986073094297
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:57 UTC
last updated: 2026-09-26 20:12:57 UTC

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

(-1206310, 99626765)
(573875/4, 1191149515/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=22; A=(3q-p)(p+q)^3=-3545129, B=-(p+3q)(p-q)^3=5484375. 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 20:12:57 UTC · history