Properties

Label 2.8.ad_d
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:  $1 - 3 x + 3 x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0953165727453$, $\pm0.639785697984$
Angle rank:  $2$ (numerical)
Number field:  4.0.271633.1
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
$A(\F_{q^r})$ 41 3895 227468 16690075 1082548871 68545207120 4400686542797 281704048420275 18014949256511252 1152968918632045975

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 62 441 4074 33036 261479 2098410 16790866 134221833 1073785982

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.