TY - JOUR ID - 1079 TI - A descent method for explicit computations on curves JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Filom, K. AD - Department of Mathematical Sciences‎, ‎Sharif University of Technology‎, ‎Tehran‎, ‎Iran. Y1 - 2017 PY - 2017 VL - 43 IS - 6 SP - 1989 EP - 2016 KW - Algebraic curves‎ KW - ‎branched covers‎ KW - ‎elliptic curves‎ DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_1079.html L1 - http://bims.iranjournals.ir/article_1079_545c2bcc6cfdf11ec7739e314d3a881f.pdf ER -