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curve #2487

y2 + xy = x3 − x2 − 999532035x + 11959794684225
a-invariants
[1, -1, 0, -999532035, 11959794684225]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1711710
discriminant (Δ)
2120925275533208063079260100
Faltings height
4.0365
naive height
73.7820
primes of bad reduction
2, 3, 5, 7, 11, 13, 19
regulator
3.028165494763023061987702204898255040367
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=-6, q=13; A=(3q-p)(p+q)^3=15435, B=-(p+3q)(p-q)^3=226347. 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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