Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 29 x + 256 x^{2} )^{2}$ |
$1 - 58 x + 1353 x^{2} - 14848 x^{3} + 65536 x^{4}$ | |
Frobenius angles: | $\pm0.138932406859$, $\pm0.138932406859$ |
Angle rank: | $1$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $51984$ | $4252083264$ | $281403980010000$ | $18446940199617456384$ | $1208928467354427809821584$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $199$ | $64879$ | $16772983$ | $4295012959$ | $1099514035879$ | $281475034856143$ | $72057595107672919$ | $18446744089846911679$ | $4722366483063773940103$ | $1208925819616127743596079$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{8}}$.
Endomorphism algebra over $\F_{2^{8}}$The isogeny class factors as 1.256.abd 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-183}) \)$)$ |
Base change
This is a primitive isogeny class.