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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We produce new explicit examples of genus‐  2   curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a family of genus‐  2   curves over   Q   whose Jacobians have a rational point of order   48  , parameterized by a rank‐  2   elliptic curve over   Q  , and we exhibit a single genus‐  2   curve over   Q   whose Jacobian has a rational point of order   70  , the largest order known. We also give new examples of genus‐  2   Jacobians with rational points of order   27  ,   28  , and   39  .  Most of our examples are produced by ‘gluing’ two elliptic curves together along their   n  ‐torsion subgroups, where   n   is either   2   or   3  . The   2  ‐gluing examples arise from techniques developed by the author in joint work with Leprévost and Poonen 15 years ago. The   3  ‐gluing examples are made possible by an algorithm for explicit   3  ‐gluing over non‐algebraically closed fields recently developed by the author in joint work with Bröker, Lauter, and Stevenhagen.

Genus‐2 Jacobians with torsion points of large order