Explicit isogenies of elliptic curves

Let E be an elliptic curve defined over a field K. The main topic of this \nthesis is to present a method for the explicit computation of all separable K- \nrational l-isogenies of E and isogenous curves for small primes l. The key tool \nfor this explicit computation is that the modular curve X0(l) parametrises l- \nisogenies of elliptic curves. In [3], Cremona and Watkins give explicit isogeny \nformulae for l 2 f2; 3; 5; 7; 13g, where the modular curve X0(l) has genus 0. \nTheir formula allow us to compute l-isogenies of E by simply substituting its \nj-invariant and twisting parameter into the formulae. We extend the work \nof Cremona and Watkins to the cases l 2 f11; 17; 19; 23; 29; 31; 41; 47; 59; 71g, \nwhere the genus of X0(l) is greater than 0 but the modular curve X+ \n0 (l) has \ngenus 0.