On the integrality of modular symbols and Kato's Euler system for elliptic curves

Abstract

Let E/Q be an elliptic curve. We investigate the de- nominator of the modular symbols attached to E. We show that one can change the curve in its isogeny class to make these denominators coprime to any given odd prime of semi-stable reduction. This has applications to the integrality of Kato's Euler system and the main conjecture in Iwasawa theory for elliptic curves.