Properties

Label 2.8.ac_j
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:  $1 - 2 x + 9 x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.263376259817$, $\pm0.604766495208$
Angle rank:  $2$ (numerical)
Number field:  4.0.31808.1
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
$A(\F_{q^r})$ 56 5152 260792 17166464 1092163576 68547612448 4388186999672 281465257697792 18013722014190392 1152880631965418272

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 79 511 4191 33327 261487 2092447 16776639 134212687 1073703759

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.