Random Weierstrass equations over Z_p have Haar-measure densities for admitting a Q_p-rational 3-torsion point or 3-isogeny given by exact rational functions depending on p modulo 3.
The proport ion of genus one curves over Q defined by a binary quartic that everywhere locally have a point
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
citation-role summary
background 1
citation-polarity summary
fields
math.NT 1years
2025 1verdicts
ACCEPT 1roles
background 1polarities
support 1representative citing papers
citing papers explorer
-
The density of elliptic curves over $\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny
Random Weierstrass equations over Z_p have Haar-measure densities for admitting a Q_p-rational 3-torsion point or 3-isogeny given by exact rational functions depending on p modulo 3.