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curve #2559

y2 + xy + y = x3 − 40131018x + 97848210556
a-invariants
[1, 0, 1, -40131018, 97848210556]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
79170
discriminant (Δ)
12189853011609000000
Faltings height
2.9232
naive height
64.1366
primes of bad reduction
2, 3, 5, 7, 13, 29
regulator
3.201398197624661163775999174172478639595
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=-29, q=1; A=(3q-p)(p+q)^3=-702464, B=-(p+3q)(p-q)^3=-702000. 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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