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Toric forms of elliptic curves and their arithmetic
2011
Journal of symbolic computation
We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural framework for the study of various forms of elliptic curves. The class both encompasses many prominent known forms and includes thousands of new forms. A powerful algorithm is described that automatically computes the most compact group operation formulas for any parameterized family of elliptic curves. The generality
doi:10.1016/j.jsc.2011.02.003
fatcat:xl7orq4jmbcjfg42bebmk5hg3u