Relation between torsion points and reduction of elliptic curves over number fields (Towards new development of mathematics via computational algebra system)

Abstract

This is a summary of our previous work on relation between torsion points and bad reduction primes of an elliptic curve E over a number field. We mainly introduce some results on the non-existence of a torsion points of E of prime order p if E has bad reduction only at certain primes related with p.