Properties

Label 4.5.ao_do_aog_bmk
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:  $( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.35241638235$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 32 256000 268745504 167772160000 99932932273952 61405122717952000 38027626991359982624 23535616807151861760000 14601971742634905262179872 9095833637090033463712000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 14 136 682 3272 16094 79736 394842 1959832 9766574

Decomposition

1.5.ae 3 $\times$ 1.5.ac

Base change

This is a primitive isogeny class.