Properties

Label 2.3.a_c
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$
Frobenius angles:  $\pm0.304086723985$, $\pm0.695913276015$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 12 144 684 9216 59532 467856 4779948 42614784 387423756 3544059024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 14 28 110 244 638 2188 6494 19684 60014

Decomposition

1.3.ac $\times$ 1.3.c

Base change

This is a primitive isogeny class.