Analogues of Vélu's formulas for isogenies on alternate models of elliptic curves (Q2796026)

The paper presents various formulas for isogenies defined on certain models of elliptic curves; namely \textit{Edward curves} NEWLINE\[NEWLINE E_d : x^2+y^2=1+dx^2y^2 \;,\qquad d\neq 0,1 NEWLINE\]NEWLINE (and their twists \(ax^2+y^2=1+dx^2y^2\)) and \textit{Huff curves} NEWLINE\[NEWLINE H_{a,b} : x(ay^2-1)=y(bx^2-1) \;, \qquad ab(a-b)\neq 0\;.NEWLINE\]NEWLINE The computation of the formulas relies on series expansions at certain points and on checking zeroes and poles of functions defined on the codomain curves (differences between the two models depend on their specific features like their identity point and their points at infinity). The final outcome can be considered as an analogue of the results of \textit{J. Vélu} [C. R. Acad. Sci., Paris, Sér. A 273, 238--241 (1971; Zbl 0225.14014)] for curves in Weierstrass form, but, as the authors point out in the final sections, it provides a more efficient (and faster) algorithm to compute explicit formulas for isogenies.