Properties

Label 3.11.ao_dt_apn
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:  $( 1 - 5 x + 11 x^{2} )( 1 - 9 x + 41 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.178435994483$, $\pm0.22822922288$, $\pm0.329700688269$
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
$A(\F_{q^r})$ 385 1773695 2583071260 3250517799375 4206404221250000 5563062240305274320 7399713440925070677335 9849451241786478150819375 13109822724019405745033009260 17449225520380929509044580000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 120 1453 15156 162173 1772565 19485758 214352756 2357916853 25937161875

Decomposition

1.11.af $\times$ 2.11.aj_bp

Base change

This is a primitive isogeny class.