New answers tagged computational-number-theory
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The equation $ax^2 +by^2 =1 \mod P$ in cyclotomic field
This problem should really be posed over a general finite field (reductions of elements in $\mathcal O_L$ modulo $P$ can be computed in polynomial time).
Over any finite field $F$, the equation $ax^2+...
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Isogenous elliptic curves and canonical modular polynomials
It turns out that restricting to $\ell \in \{2,3,5,7,13\}$ (where the modular curve $X_0(\ell)$ has genus $0$) and assuming $p \neq \ell$ is sufficient, while experiments suggest that the approach ...
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