Properties

Label 3.11.an_de_amq
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 29 x^{2} - 77 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.140218899004$, $\pm0.162126013132$, $\pm0.441671623734$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 402 1700460 2392432650 3133376425440 4190280502943712 5579403547120087500 7409873172991497980082 9851641407925845940978560 13109892206636867082884429850 17449331194613322517763378304000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 117 1349 14617 161554 1777761 19512499 214400417 2357929349 25937318952

Decomposition

1.11.ag $\times$ 2.11.ah_bd

Base change

This is a primitive isogeny class.