The masterful derivation by Harold Edwards  finally brings the vision of Abel to the wider audience it deserves. The article describes a constructive approach for improving computations along elliptic curves. The new and simple addition rules of [1, Part II] have been widely appreciated, while the calculus of [1, Part III] remains underutilized. As with the much earlier Weierstrass function, the Edwards function determines time-dependent solutions for a range of interesting Hamiltonian systems . This Demonstration shows three interrelated examples, including one that describes the oscillation of a plane pendulum. Edwards function is truly an amazing and beautiful, doubly-periodic, meromorphic function!