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curve #2554

y2 + xy + y = x3 − 5134368x + 4453877806
a-invariants
[1, 0, 1, -5134368, 4453877806]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
62790
discriminant (Δ)
91209357028881000000
Faltings height
2.6688
naive height
57.9680
primes of bad reduction
2, 3, 5, 7, 13, 23
regulator
3.018098887366123434419712058901007942913
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=-23, q=3; A=(3q-p)(p+q)^3=-256000, B=-(p+3q)(p-q)^3=-246064. 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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