Properties

Label 5.2.ah_bb_acu_fp_aiw
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $4$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0435981566527$, $\pm0.25$, $\pm0.329312442367$, $\pm0.384973271919$, $\pm0.527830414776$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 2 2840 76622 823600 23110142 761622680 25046137216 986397717600 37734169585658 1138893218916200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 17 14 21 43 87 230 548 1035

Decomposition

1.2.ac $\times$ 1.2.ab $\times$ 3.2.ae_j_ap

Base change

This is a primitive isogeny class.