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curve #2580

y2 + xy + y = x3 − x2 − 455648x + 94718531
a-invariants
[1, -1, 1, -455648, 94718531]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
6930
discriminant (Δ)
2187934777222286400
Faltings height
2.2340
naive height
50.7020
primes of bad reduction
2, 3, 5, 7, 11
regulator
2.022160351098361133976144469125659346751
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=-9, q=2; A=(3q-p)(p+q)^3=-5145, B=-(p+3q)(p-q)^3=-3993. 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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