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

• Label: 2.625.adp_fay
• 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:	$1 - 93 x + 3404 x^{2} - 58125 x^{3} + 390625 x^{4}$
Frobenius angles:	$\pm0.0504914747344$, $\pm0.162461973402$
Angle rank:	$2$ (numerical)
Number field:	4.0.10132056.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$335812$	$151870305376$	$59597561313658624$	$23283022426840033895808$	$9094947258961836567512982532$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$533$	$388785$	$244111610$	$152587615777$	$95367434170133$	$59604644978806398$	$37252902990285142469$	$23283064365475864259137$	$14551915228366668016714202$	$9094947017729212543500008625$

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 4.0.10132056.2.

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_fay	$2$	(not in LMFDB)