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curve #2558

y2 + xy + y = x3 − 3339463x + 1946476406
a-invariants
[1, 0, 1, -3339463, 1946476406]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
91770
discriminant (Δ)
746253168334407562500
Faltings height
2.7240
naive height
56.6776
primes of bad reduction
2, 3, 5, 7, 19, 23
regulator
1.887047788020050409991781388840558949457
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=-23, q=5; A=(3q-p)(p+q)^3=-221616, B=-(p+3q)(p-q)^3=-175616. 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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