The MELODIA Project

Methods for low-dimensional abelian varieties


The AVIsogenies library

As part of objectives 2 and 3, the MELODIA project will exploit data from and contribute back to the AVIsogenies library.

  1. First and foremost, we will expand on the embedded "curve-db" database to classify various types and features of isogeny graphs. This will provide us with a variety of test cases to refine our hypothesis and obtain more precise results on the structure of such graphs.
  2. Second, all algorithms designed as part of the MELODIA project will be implemented by building upon the AVIsogenies library and will be released under an open-source license.

Data on modular forms

Rahm and Tsaknias' database of dimension tables for spaces of Bianchi modular forms is available in open access on the MELODIA website, an will be extended as part of the MELODIA project.