A generalization of the conjecture of Birch and Swinnerton-Dyer is investigated using complex multiplication cycles on a particular Kuga fiber variety. A weak finiteness result consistent with the conjecture is proved. The image of complex multiplication cycles under the Abel-Jacobi map is computed explicitly. The results provide numerical evidence supporting the conjecture.They also give evidence for a relationship between complex multiplication cycles and a modular form of weight 5/2 and raise questions for further ind. © 1993 American Mathematical Society.