English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We give new parametrisations of elliptic curves in Weierstrass normal form$y^2=x^3+ax^2+bx$ with torsion groups $\mathbb{Z}/10\mathbb{Z}$ and$\mathbb{Z}/12\mathbb{Z}$ over $\mathbb{Q}$, and with $\mathbb{Z}/14\mathbb{Z}$and $\mathbb{Z}/16\mathbb{Z}$ over quadratic fields. Even though theparametrisations are equivalent to those given by Kubert and Rabarison,respectively, with the new parametrisations we found three infinite families ofelliptic curves with torsion group $\mathbb{Z}/12\mathbb{Z}$ and positive rank.Furthermore, we found elliptic curves with torsion group$\mathbb{Z}/14\mathbb{Z}$ and rank $3$, which is a new record for such curves,as well as some new elliptic curves with torsion group$\mathbb{Z}/16\mathbb{Z}$ and rank $3$.

A geometric approach to elliptic curves with torsion groups  $\mathbb{Z}/10\mathbb{Z}$, $\mathbb{Z}/12\mathbb{Z}$,  $\mathbb{Z}/14\mathbb{Z}$, and $\mathbb{Z}/16\mathbb{Z}$