Properties

Label 3.5.ah_z_acl
Base Field $\F_{5}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5}$
Dimension:  $3$
L-polynomial:  $1 - 7 x + 25 x^{2} - 63 x^{3} + 125 x^{4} - 175 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.0923731703714$, $\pm0.243942915084$, $\pm0.536165446792$
Angle rank:  $3$ (numerical)
Number field:  6.0.40529831.1
Galois group:  $A_4\times C_2$
Jacobians:  0

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 31 16151 1863379 238017287 31856571571 3880369374623 473860949307392 59429177074303943 7460168205289474927 932040174864007852511

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 27 119 611 3259 15891 77636 389475 1955639 9773147

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The endomorphism algebra of this simple isogeny class is 6.0.40529831.1.
All geometric endomorphisms are defined over $\F_{5}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.5.h_z_cl$2$3.25.b_ah_dd