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curve #2587

y2 + xy + y = x3 − 375973x + 85217756
a-invariants
[1, 0, 1, -375973, 85217756]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
46410
discriminant (Δ)
261806444735062500
Faltings height
2.1049
naive height
50.1254
primes of bad reduction
2, 3, 5, 7, 13, 17
regulator
1.674159868526776475606234253122231936179
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=-17, q=3; A=(3q-p)(p+q)^3=-71344, B=-(p+3q)(p-q)^3=-64000. 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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