# Questions tagged [isogeny]

For questions about morphisms of algebraic groups (group varieties) that are surjective and have a finite kernel.

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### Dual isogeny of purely inseparable isogeny is not always purely inseparable

Let $φ$ be purely inseparable isogeny of elliptic curves. Then, dual isogeny of $φ$ is always purely inseparable? Background Super singular elliptic curve over a field of characteristic $p$ is defined ...
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### Does the first coordinate of a morphism (isogeny) of elliptic curves only depend on the $x$-coordinate?

Let $E,E'$ be two elliptic curves over a field $k$ of characteristic $\neq 2, 3$. Assume that $E,E'$ are given by short Weierstrass equations, and let $f : E \to E'$ be a morphism given by f(x,y) = (...
Isogeny is morphism between elliptic curves which keeps base point. Then, is every isogeny between elliptic curves bijective? Let $E1$ and $E2$ be isogenous elliptic curves defined over Fq. Then #E1(...
### How to confirm $\phi(F_1(x,y))＝F_2(\phi(x),\phi(y))$,where $F_1$ and $F_2$ are formal group law of elliptic curve $E_1$, $E_2$.
This question is from Silverman's 'the arithmetic of elliptic curves',$p134$. Let $K$ be a field of characteristic $p > 0$, let $E_1/ K$ and $E_2/K$ be elliptic curves, and let $\phi : E_1 \to E_2$...