Properties

Label 5.2.ag_r_abc_be_abg
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.069353354755$, $\pm0.25$, $\pm0.25$, $\pm0.339907131295$, $\pm0.77055377654$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 2 1100 65234 3740000 28143302 896967500 26886431938 844596720000 38112217374998 1149689065827500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 3 15 39 27 51 95 191 555 1043

Decomposition

1.2.ac 2 $\times$ 3.2.ac_b_a

Base change

This is a primitive isogeny class.