Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.25$, $\pm0.833333333333$
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
$A(\F_{q^r})$ 3 45 1053 11025 40713 426465 1837041 16769025 126584289 1010700225

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 1 13 33 41 97 113 257 481 961

Decomposition

1.2.ac $\times$ 2.2.a_ac

Base change

This is a primitive isogeny class.