Algebraic Curves Databases

• • Algebraic Curves Database includes all genus g>1 curves whichhave large automorphism group G (i, e., |G|> 4(g-1) )

  • superelliptic curves   (i.e., curves with equation y^n=f(x) )

  • genus 2 curves with split Jacobians and many elliptic subcovers 

The database includes curves in characteristic 0 and in characteristic p<>2.  We only list curves over prime fields but our methods can be easily extended to any size field.  The above families of curves can be used in cryptography, factoring large numbers, integrable systems, wave equation (KdP, KP) and many other applications. While the database is private we usually make available data to researchers upon request.  The database will soon have it's own website and will be reorganized in order to make possible some public searches.  To donate to this project or to be a part of it contact  T. Shaska at shaska@oakland.edu 

The current database goes up to g<10.