Abelian variety isogeny class 1.113.ae over $\F_{113}$

• Label: 1.113.ae
• Base field: $\F_{113}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$1$
L-polynomial:	$1 - 4 x + 113 x^{2}$
Frobenius angles:	$\pm0.439752777404$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-109}) \)
Galois group:	$C_2$
Jacobians:	$6$
Isomorphism classes:	6

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:	$1$
Slopes:	$[0, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$110$	$12980$	$1444190$	$163028800$	$18424131550$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$110$	$12980$	$1444190$	$163028800$	$18424131550$	$2081952969140$	$235260577798510$	$26584441910611200$	$3004041934548288590$	$339456738980563598900$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which 0 are hyperelliptic):

• $y^2=x^3+66 x+85$
• $y^2=x^3+21 x+63$
• $y^2=x^3+61 x+61$
• $y^2=x^3+72 x+103$
• $y^2=x^3+69 x+94$
• $y^2=x^3+61 x+70$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-109}) \).

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
1.113.e	$2$	(not in LMFDB)