Polynesian Journal of Mathematics

Volume 4, Issue 13
Special volume AJAX in honor of René Schoof

Weber modular curves and modular isogenies

Leonardo Colò and David Kohel

Abstract:

We study the modular curves defined by Weber functions, and associated modular polynomials, action of ${\mathrm{SL}}_2\left(\mathbb{Z}\right)$, and parametrizations of elliptic curves with a view to the study of the isogeny graphs that they determine, particularly for supersingular elliptic curves. In addition to applications to efficient isogeny computation in cryptographic applications, we present an application to explicit Galois representations.

Citation:

Leonardo Colò and David Kohel. Weber modular curves and modular isogenies. Polynesian Journal of Mathematics, Volume 4, Issue 13, Pages 1–22. (Sept. 2026) DOI: 10.69763/polyjmath.4.13

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Milestones:

Received 3 Mar 2026
Revised 25 Jun 2026
Accepted 6 Jul 2026
Published 28 Sep 2026
Communicated by Valerio Talamanca

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