Properties

Label 2.8.ae_i
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 8 x^{2} - 32 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.583333333333$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\zeta_{12})\)
Galois group:  $V_4$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 37 4033 231361 16265089 1082163457 68720001025 4393753638913 281612466003969 18018797092896769 1152921503533105153

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 65 449 3969 33025 262145 2095105 16785409 134250497 1073741825

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.