Properties

Label 4.5.al_cg_ahp_te
Base Field $\F_{5}$
Dimension $4$
$p$-rank $4$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.20674167778$, $\pm0.540075011113$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 64 332800 235286272 159488409600 105937056318784 62857951053414400 37622750928200078656 23334330333320655667200 14573326513210221066708736 9091927125274661971438720000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 21 118 653 3455 16458 78899 391485 1955998 9762381

Decomposition

1.5.ae 2 $\times$ 2.5.ad_i

Base change

This is a primitive isogeny class.