We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Delaunay. These are notes from a short course given at the Institut Henri Poincare in December 2004.
Watkins, Mark, "Some Remarks on Heegner Point Computations" (2006). Mathematics Faculty Scholarship. 106.
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