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curve #2579

y2 + xy = x3 − 6229091x + 5983356225
a-invariants
[1, 0, 0, -6229091, 5983356225]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
98670
discriminant (Δ)
184733644634510400
Faltings height
2.4934
naive height
58.5478
primes of bad reduction
2, 3, 5, 11, 13, 23
regulator
3.398325095669385737848256075897601303271
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=-23, q=1; A=(3q-p)(p+q)^3=-276848, B=-(p+3q)(p-q)^3=-276480. 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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