Properties

Label 3.2.ac_e_ae
Base Field $\F_{2}$
Dimension $3$
$p$-rank $0$

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.25$, $\pm0.333333333333$, $\pm0.666666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7 245 637 11025 43337 156065 1865969 16769025 125599201 1145180225

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 9 13 33 41 33 113 257 481 1089

Decomposition

1.2.ac $\times$ 2.2.a_c

Base change

This is a primitive isogeny class.