Properties

Label 2.8.ah_y
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:  $1 - 7 x + 24 x^{2} - 56 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0585111942353$, $\pm0.418160225599$
Angle rank:  $2$ (numerical)
Number field:  4.0.2312.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 26 3952 258362 16132064 1055303626 68606478928 4402261596122 281525456219072 18012368433333482 1152880874334874672

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 64 506 3936 32202 261712 2099162 16780224 134202602 1073703984

Decomposition

This is a simple isogeny class.

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.ab_a