The existence of curves of genus two with elliptic differentials (Q1356240)

Given two elliptic curves \(E,E'\) and an integer \(n \geq 2\), the author shows that, unless \(E,E'\) are supersingular and of \(j\)-invariant zero (and thus the characteristic is positive), there exists a curve of genus two \(C\) and morphisms \(f:C \to E,f':C \to E'\) of degree \(n\). This is a sequel to his earlier paper [\textit{E. Kani}, The number of curves of genus two with elliptic differentials, J. Reine Angew. Math. 485, 93-121 (1997; Zbl 0867.11045)].