Properties

Label 2.2.b_b
Base Field $\F_{2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $1 + x + x^{2} + 2 x^{3} + 4 x^{4}$
Frobenius angles:  $\pm0.347634004421$, $\pm0.802798946039$
Angle rank:  $2$ (numerical)
Number field:  4.0.2873.1
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
$A(\F_{q^r})$ 9 27 108 459 549 3888 15003 70227 303588 989847

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 6 13 26 14 63 116 274 589 966

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.