Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 3 x + 7 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.190783854037$, $\pm0.524117187371$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 9 3159 206388 14294475 1096788339 70413806736 4329066970881 277316831747475 17944126622135532 1150148694100113279

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 14 49 218 1048 4199 16126 64562 261121 1046054

Decomposition

1.4.ae $\times$ 2.4.ad_h

Base change

This is a primitive isogeny class.