Abelian variety isogeny class 2.121.abq_bag over $\F_{11^{2}}$

• Label: 2.121.abq_bag
• Base field: $\F_{11^{2}}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{11^{2}}$
Dimension:	$2$
L-polynomial:	$( 1 - 11 x )^{2}( 1 - 20 x + 121 x^{2} )$
	$1 - 42 x + 682 x^{2} - 5082 x^{3} + 14641 x^{4}$
Frobenius angles:	$0$, $0$, $\pm0.136777651826$
Angle rank:	$1$ (numerical)
Jacobians:	$0$

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

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10200$	$208569600$	$3132407035800$	$45944378910720000$	$672746202824425455000$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$14242$	$1768160$	$214333918$	$25937278400$	$3138427829122$	$379749833235440$	$45949729844927038$	$5559917312303977520$	$672749994901619199202$

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 $\F_{11^{2}}$.

Endomorphism algebra over $\F_{11^{2}}$

The isogeny class factors as 1.121.aw $\times$ 1.121.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.121.aw : the quaternion algebra over \(\Q\) ramified at $11$ and $\infty$.
• 1.121.au : \(\Q(\sqrt{-21}) \).

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
2.121.ac_ahq	$2$	(not in LMFDB)
2.121.c_ahq	$2$	(not in LMFDB)
2.121.bq_bag	$2$	(not in LMFDB)
2.121.aj_w	$3$	(not in LMFDB)