Properties

Label 4.5.al_cd_agr_qe
Base Field $\F_{5}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.113143297209$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.585923223955$
Angle rank:  $3$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 52 254800 188267716 152635392000 104445396370432 61894084760981200 37743422774763944836 23522449559682318336000 14607820454067422008883092 9095901361683172330577920000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 15 91 623 3410 16215 79151 394623 1960615 9766650

Decomposition

1.5.ae 2 $\times$ 2.5.ad_f

Base change

This is a primitive isogeny class.