Properties

Label 3.11.ao_dr_apd
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:  $( 1 - 5 x + 11 x^{2} )( 1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.100899808413$, $\pm0.22822922288$, $\pm0.366706655625$
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
$A(\F_{q^r})$ 371 1696583 2479542884 3178760323375 4178308288003696 5559214858272634832 7401962814830238177481 9851006129686351637655375 13110296496198694814725288676 17449373373424107846345549955328

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 116 1399 14828 161093 1771337 19491680 214386596 2358002065 25937381651

Decomposition

1.11.af $\times$ 2.11.aj_bn

Base change

This is a primitive isogeny class.