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curve #2462

y2 + xy = x3 − x2 − 4435511634x + 86095339226388
a-invariants
[1, -1, 0, -4435511634, 86095339226388]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1711710
discriminant (Δ)
2382767701220962028494521000000
Faltings height
4.5392
naive height
78.2523
primes of bad reduction
2, 3, 5, 7, 11, 13, 19
regulator
2.733538634761924738739041722145091068871
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=-24, q=11; A=(3q-p)(p+q)^3=-125229, B=-(p+3q)(p-q)^3=385875. 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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