Properties

Label 5.2.ah_z_ack_eq_ahg
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.123548644961$, $\pm0.25$, $\pm0.456881978294$, $\pm0.583333333333$
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
$A(\F_{q^r})$ 1 1235 24700 722475 52048721 1586234000 36003483587 1172808839475 37340819850100 1195932570943175

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 5 10 46 87 136 274 545 1086

Decomposition

1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_c

Base change

This is a primitive isogeny class.