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curve #2592

y2 + xy = x3 − 32889199005845x − 5906812809786954975
a-invariants
[1, 0, 0, -32889199005845, -5906812809786954975]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
40682217030
discriminant (Δ)
2261805885819848354828861651782100769000000
Faltings height
6.8167
naive height
104.9861
primes of bad reduction
2, 3, 5, 7, 13, 17, 29, 167, 181
regulator
111.49324729911060906355474814191521247455169
submitted by
Natanael Wildner Fraga
submitted at
later contributions
  • rank ≥ 2 → ≥ 3 · Tom Fisher ·

Witness: 3 independent points log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=58; A=(3q-p)(p+q)^3=24009831, B=-(p+3q)(p-q)^3=45862375. 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 · history

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