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curve #2581

y2 + xy = x3 − x2 − 2994759x + 1995489513
a-invariants
[1, -1, 0, -2994759, 1995489513]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
6930
discriminant (Δ)
35596085895562500
Faltings height
2.3252
naive height
56.3507
primes of bad reduction
2, 3, 5, 7, 11
regulator
2.550393544124009643812867570297125497204
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=-21, q=1; A=(3q-p)(p+q)^3=-192000, B=-(p+3q)(p-q)^3=-191664. 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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