A descent method for explicit computations on curves

‎It is shown that the knowledge of a surjective morphism X→Y of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of j(nτ) (for some small n) in terms of j(τ) for the elliptic curve ‎with period lattice (1,τ)‎, ‎the period matrix for the Jacobian of a family of genus-2 curves‎ ‎complementing the classic calculations of Bolza‎ ‎and explicit general formulae for branched covers of an elliptic curve with exactly one ramification point.