Properties

Label 3.4.ah_w_abw
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 3 x + 6 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.15043295046$, $\pm0.544835058382$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 8 2736 179144 13816800 1097162168 70028464464 4339561514408 280096850059200 18042305355475352 1151005491361897776

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 12 40 208 1048 4176 16168 65216 262552 1046832

Decomposition

1.4.ae $\times$ 2.4.ad_g

Base change

This is a primitive isogeny class.