Properties

Label 4.5.al_ci_aik_vz
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:  $( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.0878807261908$, $\pm0.384619558242$, $\pm0.450170915301$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 63 343413 233700012 128379112029 87029776331568 59175145450918224 37623882916287319491 23355899060757619121325 14547860733152098732413852 9095463641330437680639848448

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 121 517 2840 15511 78899 391845 1952581 9766180

Decomposition

2.5.ag_r $\times$ 2.5.af_n

Base change

This is a primitive isogeny class.