Properties

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

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 17 x^{2} - 32 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.270666572915$, $\pm0.484916916854$
Angle rank:  $2$ (numerical)
Number field:  4.0.83088.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 46 5428 285982 16761664 1076284126 68875332916 4394281635118 281228070198528 18012491319904846 1153026669191799988

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 83 557 4095 32845 262739 2095357 16762495 134203517 1073839763

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.