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A rational perfect cuboid is a rectangular parallelepiped whose edges andface diagonals are given by rational numbers and whose space diagonal is equalto unity. Recently it was shown that the Diophantine equations describing sucha cuboid lead to a couple of parametric families of elliptic curves. Two andthree descent methods for calculating their ranks are discussed in the presentpaper. The elliptic curves in each parametric family are subdivided into twosubsets admitting 2-descent and 3-descent methods respectively.

Two and three descent for elliptic curves associated with perfect cuboids