Integrality Properties in the Moduli Space of Elliptic Curves: Isogeny Case.

For a fixed j –invariant j 0 of an elliptic curve without complex multiplication we bound the number of j –invariants j that are algebraic units and such that elliptic curves corresponding to j and j 0 are isogenous. Our bounds are explicit. We also modify the problem slightly by fixing a singular modulus α and looking at all j such that |$j-\alpha$| is an algebraic unit and such that elliptic curves corresponding to j and j 0 are isogenous. The number of such j can again be bounded explicitly. [ABSTRACT FROM AUTHOR]