Properties

Label 4.5.al_ci_aii_vq
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 73 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0229621162481$, $\pm0.14758361765$, $\pm0.333082169302$, $\pm0.478604549684$
Angle rank:  $4$ (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
$A(\F_{q^r})$ 66 358380 245992626 139189057920 91763628038346 59543280160366860 37270822609601606784 23256270099354103764480 14555004246562122843625026 9098524113569455041140805900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 127 569 3005 15613 78164 390177 1953541 9769465

Decomposition

1.5.ae $\times$ 3.5.ah_bb_acv

Base change

This is a primitive isogeny class.