Timeline for Reference describing supersingular elliptic curves over algebraically closed field in characteristic 2
Current License: CC BY-SA 4.0
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| Oct 7, 2020 at 12:18 | comment | added | Ben Smith | Another explicit approach: Let $E: y^2 + (a_1x + a_3)y = x^3 + a_2x^2 + a_4x + a_6$ be an elliptic curve over $\mathbb{F}_2[a_1,a_2,a_3,a_4,a_6]$. The $2$-division polynomial $\Psi_2(x)$ is $a_1^2x^2 + a_3^2$, and $j(E) = a_1^{12}/(a_1^3(\cdots) + a_3^4)$. Now $E$ is supersingular if and only if $\Psi_2$ has no roots (over the algebraic closure), which is precisely when $a_1 = 0$, and then this forces $j(E) = 0$. | |
| Jul 22, 2020 at 20:52 | review | First posts | |||
| Jul 22, 2020 at 20:52 | |||||
| Jul 22, 2020 at 20:51 | history | answered | Sarah Arpin | CC BY-SA 4.0 |