curve #2457

y² + xy + y = x³ − x² − 28020901892x + 1805317195929959

a-invariants: [1, -1, 1, -28020901892, 1805317195929959]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2792790
discriminant (Δ): 126079078290377526282969000000
Faltings height: 4.6530
naive height: 83.7823
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31
regulator: 3.225801813453182407010403861185500554729
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:45 UTC
last updated: 2026-09-26 20:02:45 UTC

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

(-127701, 57519157)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=2; A=(3q-p)(p+q)^3=-1161849, B=-(p+3q)(p-q)^3=-1157625. 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 20:02:46 UTC · history