Properties

Label 3.2.ag_s_abg
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:  $( 1 - 2 x + 2 x^{2} )^{3}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.25$
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
$A(\F_{q^r})$ 1 125 2197 15625 68921 274625 1442897 11390625 111284641 1076890625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 21 41 57 65 81 161 417 1025

Decomposition

1.2.ac 3

Base change

This is a primitive isogeny class.