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curve #2490

y2 + xy + y = x3 − 2584023369x + 50555712379576
a-invariants
[1, 0, 1, -2584023369, 50555712379576]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1820910
discriminant (Δ)
105182336548826929413648900
Faltings height
4.0589
naive height
76.6314
primes of bad reduction
2, 3, 5, 7, 13, 23, 29
regulator
3.149508767268569974767868497112078096538
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=-10, q=13; A=(3q-p)(p+q)^3=1323, B=-(p+3q)(p-q)^3=352843. 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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