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curve #2455

y2 + xy = x3 − 8172046730x + 282187580196900
a-invariants
[1, 0, 0, -8172046730, 282187580196900]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
6670290
discriminant (Δ)
527649087306165561000000000000
Faltings height
4.5271
naive height
80.0856
primes of bad reduction
2, 3, 5, 11, 17, 29, 41
regulator
2.631366347791889527840284490799506265069
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=4; A=(3q-p)(p+q)^3=-640625, B=-(p+3q)(p-q)^3=-610929. 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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