Abelian variety isogeny class 1.121.v over $\F_{11^{2}}$

• Label: 1.121.v
• Base field: $\F_{11^{2}}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: no
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{11^{2}}$
Dimension:	$1$
L-polynomial:	$1 + 21 x + 121 x^{2}$
Frobenius angles:	$\pm0.903658651096$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-43}) \)
Galois group:	$C_2$
Jacobians:	$1$
Isomorphism classes:	1

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$143$	$14443$	$1773200$	$214348563$	$25937443103$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$143$	$14443$	$1773200$	$214348563$	$25937443103$	$3138429236800$	$379749813282983$	$45949730185808163$	$5559917309181606800$	$672749994984092571403$

Jacobians and polarizations

This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{11^{2}}$.

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

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-43}) \).

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{11^{2}}$.

Subfield	Primitive Model
$\F_{11}$	1.11.ab
$\F_{11}$	1.11.b

Twists

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

Twist	Extension degree	Common base change
1.121.av	$2$	(not in LMFDB)