Properties

Label 5.2.ag_r_aba_w_aq
Base Field $\F_{2}$
Dimension $5$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.209784688372$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.790215311628$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 2000 166972 9000000 66439844 1586234000 24004034492 656100000000 29085798910324 1000750150250000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 21 55 57 87 81 127 417 903

Decomposition

1.2.ac 3 $\times$ 2.2.a_ab

Base change

This is a primitive isogeny class.