Properties

Label 5.2.ag_p_aq_af_be
Base Field $\F_{2}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0247483856139$, $\pm0.177336015878$, $\pm0.25$, $\pm0.344002682545$, $\pm0.858081718947$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 1 305 65572 1923025 27087101 1039971920 23489558261 1102972142025 30935369378212 1058347887449525

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 -1 15 27 27 65 81 259 447 959

Decomposition

1.2.ac $\times$ 4.2.ae_f_c_al

Base change

This is a primitive isogeny class.