Properties

Label 2.2.b_c
Base Field $\F_{2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$
Frobenius angles:  $\pm0.384973271919$, $\pm0.75$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 10 40 70 400 550 3640 20590 64800 282310 992200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 8 10 24 14 56 158 256 550 968

Decomposition

1.2.ab $\times$ 1.2.c

Base change

This is a primitive isogeny class.