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

• Label: 1.113.aj
• 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:	$1 - 9 x + 113 x^{2}$
Frobenius angles:	$\pm0.360863062134$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-371}) \)
Galois group:	$C_2$
Jacobians:	$8$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$105$	$12915$	$1445220$	$163051875$	$18424130025$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$105$	$12915$	$1445220$	$163051875$	$18424130025$	$2081949246720$	$235260550551705$	$26584442234791875$	$3004041940452538020$	$339456738979889529075$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):

• $y^2=x^3+20 x+60$
• $y^2=x^3+86 x+86$
• $y^2=x^3+104 x+104$
• $y^2=x^3+73 x+106$
• $y^2=x^3+39 x+4$
• $y^2=x^3+23 x+69$
• $y^2=x^3+87 x+87$
• $y^2=x^3+29 x+29$

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 \(\Q(\sqrt{-371}) \).

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.j	$2$	(not in LMFDB)