Properties

Label 2.8.ac_f
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:  $1 - 2 x + 5 x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.210521847689$, $\pm0.64346226568$
Angle rank:  $2$ (numerical)
Number field:  4.0.45072.1
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
$A(\F_{q^r})$ 52 4576 249028 17370496 1094814292 68658015712 4398633723172 281522725406208 18008993695440436 1152840596841378016

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 71 487 4239 33407 261911 2097431 16780063 134177455 1073666471

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.