Properties

Label 4.3.ah_z_aci_ek
Base Field $\F_{3}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.593214749339$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 10 8820 595840 59623200 4887498550 302705786880 22780004400310 1922914262505600 152621475670814080 12059264472339338100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 11 30 107 327 782 2181 6803 20010 58571

Decomposition

1.3.ad 2 $\times$ 1.3.ac $\times$ 1.3.b

Base change

This is a primitive isogeny class.