Properties

Label 4.5.an_db_aln_bei
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0878807261908$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.450170915301$
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
$A(\F_{q^r})$ 36 248400 224644212 144731750400 97001204486976 62083954900328400 38123717990186149812 23430229459787612160000 14569261124430772495455876 9101269404942073078210560000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 15 113 591 3178 16263 79933 393087 1955453 9772410

Decomposition

1.5.ae 2 $\times$ 2.5.af_n

Base change

This is a primitive isogeny class.