Properties

Label 2.8.af_q
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

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

Newton polygon

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 36 4536 260604 16447536 1082818836 69251343336 4403912248044 281437900380000 18015412792860036 1152981041856108696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 72 508 4016 33044 264168 2099948 16775008 134225284 1073797272

Decomposition

1.8.af $\times$ 1.8.a

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.b_e