Beshaj, LubjanaElezi, ArturShaska, Tony2017-11-132017-11-132017-11-02http://hdl.handle.net/10323/4599We prove that for $N=2,3, 5, 7$ there are only finitely many genus two curves $\X$ (up to isomorphism) defined over $\Q$ with $(2, 2)$-split Jacobian and $\Aut (\X)\iso V_4$, such that their elliptic subcovers are $N$-isogenous. Also, there are only finitely many genus two curves $\X$ (up to isomorphism) defined over $\Q$ with $(3, 3)$-split Jacobian such that their elliptic subcovers are $5$-isogenous.en-USIsogenyCryptographyArticle