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curve #2442

y2 + xy + y = x3 − 11899999898x + 410152668743756
a-invariants
[1, 0, 1, -11899999898, 410152668743756]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1591590
discriminant (Δ)
35176530349719088580250000000000
Faltings height
4.7709
naive height
81.2130
primes of bad reduction
2, 3, 5, 7, 11, 13, 53
regulator
3.638481338281048052144651734629107573170
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=-32, q=7; A=(3q-p)(p+q)^3=-828125, B=-(p+3q)(p-q)^3=-652509. 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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