New elliptic potentials

We construct all tangential covers as zeroes of a particular set of polynomials. The resulting pointed curves give rise, through the Krichever dictionary, to elliptic KP solitons. We then give a criterion to detect the so-called hyperelliptic-tangential covers, which give rise to elliptic KdV solitons. Finally we construct new examples of the latter covers and write down the corresponding (doubly periodic finite-gap) source potentials.Dedicated to the memory of J.-L. Verdier