Given a rational elliptic curve, one can use Tate's algorithm to determine local data of the elliptic curve at each prime. This includes the Néron type, conductor, and Tamagawa number. It is well known that the isogenous elliptic curves have the same conductor. For an elliptic curve with non-trivial torsion, we investigate how the Néron type and Tamagawa number change along it's isogeny graph.
Local data for elliptic curves with non-trivial torsion
Bella Tobin, Oklahoma State UniversityAuthors: Alexander J. Barrios, Manami Roy, Nandita Sahajpal, Bella Tobin, Hanneke Wiersema, Darwin Xavier Tallana Chimarro}
2022 AWM Research Symposium
Rethinking Number Theory