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curve #2334

y2 + xy = x3 − 457615361060x + 73518064556835600
a-invariants
[1, 0, 0, -457615361060, 73518064556835600]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
25025910
discriminant (Δ)
3798202426047728168730624000000000000
Faltings height
5.7198
naive height
92.1615
primes of bad reduction
2, 3, 5, 7, 13, 89, 103
regulator
7.939729016426670158511778492965385923626
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=-7, q=32; A=(3q-p)(p+q)^3=1609375, B=-(p+3q)(p-q)^3=5279391. 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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