Properties

Label 3.2.ae_i_am
Base Field $\F_{2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.25$, $\pm0.583333333333$
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

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 65 325 4225 54161 274625 1632737 16769025 142869025 1073741825

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 5 5 17 49 65 97 257 545 1025

Decomposition

1.2.ac $\times$ 2.2.ac_c

Base change

This is a primitive isogeny class.