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curve #2248

y2 + xy = x3 − 52322175439800x + 145669265717792040000
a-invariants
[1, 0, 0, -52322175439800, 145669265717792040000]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
17250870
discriminant (Δ)
373970470890111146078995673911296000000
Faltings height
6.5131
naive height
106.3789
primes of bad reduction
2, 3, 5, 7, 13, 71, 89
regulator
4.802674271271233051092287292269284136064
submitted by
Natanael Wildner Fraga
submitted at
last updated

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Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=40; A=(3q-p)(p+q)^3=-123201, B=-(p+3q)(p-q)^3=50052799. 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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