Properties

Label 3.5.ah_y_ach
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:  $1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.0749012311065$, $\pm0.225515375241$, $\pm0.553262127050$
Angle rank:  $3$ (numerical)
Number field:  6.0.29215664.1
Galois group:  $S_4\times C_2$
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
$A(\F_{q^r})$ 29 14819 1730372 235814747 31945643129 3865810242224 473141662652821 59463876907244187 7456146350377582004 931267264837529756339

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 25 110 605 3269 15832 77517 389701 1954586 9765045

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The endomorphism algebra of this simple isogeny class is 6.0.29215664.1.
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_y_ch$2$3.25.ab_ak_db