Properties

Label 3.11.an_dd_amk
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:  $( 1 - x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.451829325548$
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
$A(\F_{q^r})$ 396 1667952 2355076944 3115894459392 4187575203146676 5579766049572000000 7409873167779616546716 9851755237142869229617152 13110200328368082527594077104 17449545804474034197334210288752

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 115 1328 14535 161449 1777876 19512499 214402895 2357984768 25937637955

Decomposition

1.11.ag 2 $\times$ 1.11.ab

Base change

This is a primitive isogeny class.