Timeline for Number of points of elliptic curve over $\mathbb{F}_p$ with CM by $\sqrt{-2}$ when $p\equiv 1\bmod 8$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 11, 2017 at 15:37 | vote | accept | Eduardo R. Duarte | ||
| Jul 7, 2017 at 20:55 | comment | added | Henri Cohen | I should add that I just learnt that Rubin--Silverberg published a paper on this subject in Math Comp 2009, including proofs this time. | |
| Jul 7, 2017 at 1:30 | comment | added | Jeremy Rouse | I'm fortunate to have purchased an electronic copy of GTM239. The basic CM elliptic curve for $\mathbb{Z}[\sqrt{-2}]$ is isomorphic to $E : y^{2} = x^{3} + 4x^{2} + 2x$, and for this curve Theorem 8.5.8 gives that $a_{p}(E) \equiv 2 \pmod{8}$ when $p \equiv 1 \text{ or } 11 \pmod{16}$ and $a_{p}(E) \equiv -2 \pmod{8}$ when $p \equiv 3 \text{ or } 9 \pmod{16}$. | |
| Jul 6, 2017 at 22:26 | history | answered | Henri Cohen | CC BY-SA 3.0 |