Properties

Label 3.11.ar_ez_avi
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.22822922288$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 252 1388016 2368889712 3209092992000 4220866870857252 5577953538155040000 7405933879055373747372 9851080156429017397248000 13110196369485198477966674832 17449396436707045459740886653936

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 91 1336 14967 162725 1777300 19502135 214388207 2357984056 25937415931

Decomposition

1.11.ag 2 $\times$ 1.11.af

Base change

This is a primitive isogeny class.