Properties

Label 3.11.ao_du_aps
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 4 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.22822922288$, $\pm0.22822922288$, $\pm0.2939628337$
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
$A(\F_{q^r})$ 392 1812608 2635337600 3285352000000 4217009424478312 5560429767977369600 7394930309112088549912 9846830536158121632000000 13109168384776327428357430400 17449341236759812446518301035648

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 122 1480 15314 162578 1771724 19473158 214295714 2357799160 25937333882

Decomposition

1.11.af 2 $\times$ 1.11.ae

Base change

This is a primitive isogeny class.