Properties

Label 4.3.ai_be_acu_ff
Base Field $\F_{3}$
Dimension $4$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

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

Newton polygon

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

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
$A(\F_{q^r})$ 5 5145 439040 56517825 5473190525 346961018880 24589833484445 1956789130794225 151162379345089280 11912402839226961225

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 20 102 356 882 2348 6918 19820 57846

Decomposition

1.3.ad 3 $\times$ 1.3.b

Base change

This is a primitive isogeny class.