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Evaluation of Modular Polynomials from Supersingular Elliptic Curves

open access: yes
We present several new algorithms to evaluate modular polynomials of level $\ell$ modulo a prime $p$ on an input $j$. More precisely, we introduce two new generic algorithms, sharing the following similarities: they are based on a CRT approach; they make use of supersingular curves and the Deuring correspondence; and, their memory requirements are ...
Santos, Maria Corte-Real   +4 more
openaire   +2 more sources

Categorical Torelli theorems: results and open problems. [PDF]

open access: yesRend Circ Mat Palermo, 2023
Pertusi L, Stellari P.
europepmc   +1 more source

On a certain supersingular elliptic curve

open access: yesOn a certain supersingular elliptic curve
In this note, by means of determination of the number of rational points, it is shown that if F is a finite prime field of characteristic p satisfying p≡5(mod 8) then the elliptic curve Y^2=X(X^2+X+r) defined over F is supersingular where r=1/8∈F. As an application, it is also shown that the following equality [numerical formula] holds where n=(p-1)/4.
openaire  

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