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curve #2472

y2 + xy + y = x3 − 3467591524x + 76221463442066
a-invariants
[1, 0, 1, -3467591524, 76221463442066]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
7048470
discriminant (Δ)
158664499366388223738518960400
Faltings height
4.3747
naive height
77.5138
primes of bad reduction
2, 3, 5, 11, 13, 31, 53
regulator
3.116160948620959312061922445112427960628
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=-20, q=11; A=(3q-p)(p+q)^3=-38637, B=-(p+3q)(p-q)^3=387283. 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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