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curve #2530

y2 + xy = x3 − 35633466x + 81769961700
a-invariants
[1, 0, 0, -35633466, 81769961700]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
214890
discriminant (Δ)
7001172374869514649600
Faltings height
3.0954
naive height
63.7800
primes of bad reduction
2, 3, 5, 13, 19, 29
regulator
2.111921546454282006682368188730322760303
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=-29, q=3; A=(3q-p)(p+q)^3=-667888, B=-(p+3q)(p-q)^3=-655360. 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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