Abelian variety isogeny class 2.131.abp_bag over $\F_{131}$

• Label: 2.131.abp_bag
• Base field: $\F_{131}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{131}$
Dimension:	$2$
L-polynomial:	$( 1 - 21 x + 131 x^{2} )( 1 - 20 x + 131 x^{2} )$
	$1 - 41 x + 682 x^{2} - 5371 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.130292526609$, $\pm0.161711276416$
Angle rank:	$2$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12432$	$289118592$	$5051336971968$	$86735375216985600$	$1488396460104342232752$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$16845$	$2246944$	$294517481$	$38579993501$	$5053921100982$	$662062718510711$	$86730204408385681$	$11361656661155306464$	$1488377021748641207805$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{131}$.

Endomorphism algebra over $\F_{131}$

The isogeny class factors as 1.131.av $\times$ 1.131.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.131.av : \(\Q(\sqrt{-83}) \).
• 1.131.au : \(\Q(\sqrt{-31}) \).

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
2.131.ab_agc	$2$	(not in LMFDB)
2.131.b_agc	$2$	(not in LMFDB)
2.131.bp_bag	$2$	(not in LMFDB)