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curve #2534

y2 + xy + y = x3 − 16428889x + 21675529736
a-invariants
[1, 0, 1, -16428889, 21675529736]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
903210
discriminant (Δ)
80803266865888222448100
Faltings height
3.1171
naive height
61.4573
primes of bad reduction
2, 3, 5, 7, 11, 17, 23
regulator
3.161083984359885468832723030391237380126
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=3; A=(3q-p)(p+q)^3=-30613, B=-(p+3q)(p-q)^3=-24565. 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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