T. Nara

activity

20102025

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2017

The Mordell-Weil bases for the elliptic curve of the form $y^{2} = x^{3} - m^{2} x + n^{2}$

Yasutsugu Fujita, Tadahisa Nara

Let $E_{m, n}$ be an elliptic curve over $Q$ of the form $y^{2} = x^{3} - m^{2} x + n^{2}$ , where $m$ and $n$ are positive integers. Brown and Myers showed that the curve $E_{1, n}$ has ra…

math.NT2011

Lower bounds of the canonical height on quadratic twists of elliptic curves

T. Nara

We compute a lower bound of the canonical height on quadratic twists of certain elliptic curves. Also we show a simple method for constructing families of quadratic twists with an…

math.NT2010

On the Mordell--Weil group of the elliptic curve y^2=x^3+n

Yasutsugu Fujita, Tadahisa Nara

We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We show that the points are inde…

The Mordell-Weil bases for the elliptic curve of the form y2=x3−m2x+n2

Lower bounds of the canonical height on quadratic twists of elliptic curves

On the Mordell--Weil group of the elliptic curve y^2=x^3+n

The Mordell-Weil bases for the elliptic curve of the form $y^{2} = x^{3} - m^{2} x + n^{2}$