Properties

Label 3.11.ao_dr_apf
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:  $( 1 - 3 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.270299311731$, $\pm0.350615407277$
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
$A(\F_{q^r})$ 369 1688175 2464372404 3154133836575 4152184991334864 5541238200229477200 7393628399371374078819 9848506476570552624992175 13109914968524435938233985524 17449358250960962865742500000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 116 1393 14716 160083 1765601 19469728 214332196 2357933443 25937359171

Decomposition

1.11.ad $\times$ 2.11.al_bz

Base change

This is a primitive isogeny class.