<p>We introduce new types of formula for isogenies between elliptic curves in the Weierstrass model. Elliptic curves and isogenies (morphisms between elliptic curves) are important mathematical concepts that have attracted interest of both mathematicians and cryptographers. Given a Weierstrass equation defining an elliptic curve and a finite subgroup on the curve, the well-known Vélu’s formula shows how to explicitly write down an isogeny between two Weierstrass elliptic curves with the given subgroup as its kernel. The Vélu’s formula is described by equations involving summations of the coordinates of points. Several prior works have developed a different type of isogeny formula described by products of the coordinates of points on various alternative models of elliptic curves. In this work, we give a family of new types of formula for isogenies between elliptic curves, subsuming the sum type and product type as special cases.</p>