Properties

Label 3.5.ah_bb_acu
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:  $1 - 7 x + 27 x^{2} - 72 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.0767028971338$, $\pm0.313688588913$, $\pm0.486729365003$
Angle rank:  $3$ (numerical)
Number field:  6.0.31554496.1
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
$A(\F_{q^r})$ 34 18428 2081752 227696368 29704311514 3809173155584 475438285000706 59497009954413568 7461745622541171448 932853866069718042428

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 31 134 583 3039 15604 77895 389919 1956050 9781671

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The endomorphism algebra of this simple isogeny class is 6.0.31554496.1.
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_bb_cu$2$3.25.f_aj_adq