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curve #2576

y2 + xy + y = x3 − 687089x − 116077264
a-invariants
[1, 0, 1, -687089, -116077264]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
51870
discriminant (Δ)
14944558319037792900
Faltings height
2.3764
naive height
51.9343
primes of bad reduction
2, 3, 5, 7, 13, 19
regulator
2.503003782291380187994058816762672096120
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=-10, q=3; A=(3q-p)(p+q)^3=-6517, B=-(p+3q)(p-q)^3=-2197. 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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