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curve #2488

y2 + xy = x3 − 1486402245x + 22048148081025
a-invariants
[1, 0, 0, -1486402245, 22048148081025]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
2381190
discriminant (Δ)
172300010934522515625000000
Faltings height
3.9896
naive height
74.9725
primes of bad reduction
2, 3, 5, 7, 17, 23, 29
regulator
3.227340082530063723860144340104583476142
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=-23, q=2; A=(3q-p)(p+q)^3=-268569, B=-(p+3q)(p-q)^3=-265625. 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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