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We define a three parameter family of Bell pseudo-involutions in the Riordangroup. The defining sequences have generating functions that are expressible ascontinued fractions. We indicate that the Hankel transforms of the definingsequences, and of the $A$ sequences of the corresponding Riordan arrays, can beassociated with Somos $4$ sequence. We give examples where these sequences canbe associated with elliptic curves, and we exhibit instances where ellipticcurves can give rise to associated Riordan pseudo-involutions. In the case of aparticular one parameter family of elliptic curves, we show how we canassociate to each such curve a unique Bell pseudo-involution.

Riordan Pseudo-Involutions, Continued Fractions and Somos $4$ Sequences