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curve #2339

y2 + xy + y = x3 − 425062399429x + 105898132550674556
a-invariants
[1, 0, 1, -425062399429, 105898132550674556]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
142486890
discriminant (Δ)
70534034587332786446414562771656100
Faltings height
5.5128
naive height
91.9401
primes of bad reduction
2, 3, 5, 7, 13, 19, 41, 67
regulator
8.297102343981355045623689847082818766954
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=-14, q=27; A=(3q-p)(p+q)^3=208715, B=-(p+3q)(p-q)^3=4617707. 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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