Properties

Label 2.8.ae_n
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:  $1 - 4 x + 13 x^{2} - 32 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.193271217563$, $\pm0.536415660845$
Angle rank:  $2$ (numerical)
Number field:  4.0.257936.1
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
$A(\F_{q^r})$ 42 4788 260946 16700544 1092097482 69163737300 4396395463698 281371366531584 18014939092520874 1152881830255664628

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 75 509 4079 33325 263835 2096365 16771039 134221757 1073704875

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.