Abelian variety isogeny class 2.625.adp_fax over $\F_{5^{4}}$

• Label: 2.625.adp_fax
• Base field: $\F_{5^{4}}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{5^{4}}$
Dimension:	$2$
L-polynomial:	$1 - 93 x + 3403 x^{2} - 58125 x^{3} + 390625 x^{4}$
Frobenius angles:	$\pm0.0431458011821$, $\pm0.164652188420$
Angle rank:	$2$ (numerical)
Number field:	4.0.38207421.1
Galois group:	$D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$335811$	$151869517317$	$59597493181061283$	$23283019225214002927701$	$9094947149560580455789122096$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$533$	$388783$	$244111331$	$152587594795$	$95367433022978$	$59604644927812255$	$37252902988338390767$	$23283064365410070544627$	$14551915228364663736168521$	$9094947017729156894965536958$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5^{4}}$.

Endomorphism algebra over $\F_{5^{4}}$

The endomorphism algebra of this simple isogeny class is 4.0.38207421.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.625.dp_fax	$2$	(not in LMFDB)