For each of the 15 torsion groups admissible over Q by Mazur’s theorem, the table gives the best known lower bound for the maximal Mordell-Weil rank of an elliptic curve over Q with that torsion, linking to the record curves with their torsion points and independent points of infinite order. Companion pages on the same site cover infinite families of high generic rank, the history of rank records, and records over quadratic fields.