%0 Journal Article
%T A descent method for explicit computations on curves
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Filom, K.
%D 2017
%\ 11/30/2017
%V 43
%N 6
%P 1989-2016
%! A descent method for explicit computations on curves
%K Algebraic curves
%K branched covers
%K elliptic curves
%R
%X It is shown that the knowledge of a surjective morphism $X\to Y$ of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of $j(n\tau)$ (for some small $n$) in terms of $j(\tau)$ for the elliptic curve with period lattice $(1,\tau)$, 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.
%U http://bims.iranjournals.ir/article_1079_545c2bcc6cfdf11ec7739e314d3a881f.pdf