Properties

Label 5.2.ah_z_acj_el_agw
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:  $( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.00978468837242$, $\pm0.190215311628$, $\pm0.25$, $\pm0.409784688372$, $\pm0.609784688372$
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
$A(\F_{q^r})$ 1 1205 24583 1090525 38101136 918297965 28940657243 1030791493125 27499042761151 885180832006400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 8 18 41 54 108 242 386 781

Decomposition

1.2.ac $\times$ 4.2.af_n_az_bn

Base change

This is a primitive isogeny class.