Properties

Label 4.5.al_cf_ahh_se
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.177952114464$, $\pm0.556618995437$
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
$A(\F_{q^r})$ 60 306000 219018060 158238720000 106436408884800 62860964749362000 37723253866119092940 23415883237073387520000 14587645433752853450921340 9090152629464840455232000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 19 109 647 3470 16459 79109 392847 1957915 9760474

Decomposition

1.5.ae 2 $\times$ 2.5.ad_h

Base change

This is a primitive isogeny class.