Using the principle of symmetric criticality [Palais 1979], we construct torus knots and links that extremize the Möbius-invariant energy introduced by O'Hara  and Freedman, He and Wang . The critical energies are explicitly computable using the calculus of residues, a result obtained in collaboration with Gil Stengle.
Experiments with a discretized version of the Möbius energy--applicable to the study of arbitrary knots and links--are also described, and confirm the results of the analytic calculations.
"Torus knots extremizing the Möbius energy." Experiment. Math. 2 (1) 1 - 9, 1993.