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curve #2549

y2 + xy = x3 − 5557266x − 3547208700
a-invariants
[1, 0, 0, -5557266, -3547208700]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
6630
discriminant (Δ)
5549773448629762560000
Faltings height
2.8783
naive height
58.2055
primes of bad reduction
2, 3, 5, 13, 17
regulator
2.534009439721264035146565192731875931838
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=-13, q=4; A=(3q-p)(p+q)^3=-18225, B=-(p+3q)(p-q)^3=-4913. 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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