Properties

Label 2.8.ae_p
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:  $1 - 4 x + 15 x^{2} - 32 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.230612053552$, $\pm0.513287349306$
Angle rank:  $2$ (numerical)
Number field:  4.0.11225.1
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
$A(\F_{q^r})$ 44 5104 273284 16761536 1086807964 69076356976 4394167627124 281223777131264 18012516853887116 1152945571357351024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 79 533 4095 33165 263503 2095301 16762239 134203709 1073764239

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.