Properties

Label 4.5.am_ct_akj_bbk
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.10143524516$, $\pm0.14758361765$, $\pm0.306436956418$, $\pm0.413672014132$
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
$A(\F_{q^r})$ 58 365980 289808194 156569171840 94128265961138 59931647673780220 37696051384494647986 23438944479771914595840 14584359406912159084235392 9101614396243900551995791900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 24 147 640 3084 15711 79052 393232 1957476 9772784

Decomposition

1.5.ae $\times$ 3.5.ai_bi_adp

Base change

This is a primitive isogeny class.