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

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

Invariants

Base field:	$\F_{5^{4}}$
Dimension:	$2$
L-polynomial:	$( 1 - 47 x + 625 x^{2} )^{2}$
	$1 - 94 x + 3459 x^{2} - 58750 x^{3} + 390625 x^{4}$
Frobenius angles:	$\pm0.110824686604$, $\pm0.110824686604$
Angle rank:	$1$ (numerical)

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$335241$	$151840370889$	$59596980471005184$	$23283022119922727318025$	$9094947648106872037487293161$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$532$	$388708$	$244109230$	$152587613764$	$95367438250612$	$59604645259098718$	$37252903003222179700$	$23283064365958988169604$	$14551915228382110095331342$	$9094947017729642002919493028$

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 isogeny class factors as 1.625.abv^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-291}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.625.a_abkx	$2$	(not in LMFDB)
2.625.dq_fdb	$2$	(not in LMFDB)
2.625.bv_ciy	$3$	(not in LMFDB)