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curve #2468

y2 + xy + y = x3 − 6820454768x + 216476870541806
a-invariants
[1, 0, 1, -6820454768, 216476870541806]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
4576530
discriminant (Δ)
61201836746231231285156250000
Faltings height
4.4173
naive height
79.5432
primes of bad reduction
2, 3, 5, 7, 19, 31, 37
regulator
8.124954917217048157333758440317236336372
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=-28, q=3; A=(3q-p)(p+q)^3=-578125, B=-(p+3q)(p-q)^3=-566029. 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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