Properties

Label 2.8.aj_bk
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 8 x^{2} )( 1 - 4 x + 8 x^{2} )$
Frobenius angles:  $\pm0.154919815756$, $\pm0.25$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20 3640 276860 17508400 1091278100 68981883880 4399611554540 281437900380000 18013213645806980 1152910673773058200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 56 540 4272 33300 263144 2097900 16775008 134208900 1073731736

Decomposition

1.8.af $\times$ 1.8.ae

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^3}$.

SubfieldPrimitive Model
$\F_{2}$2.2.d_g