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

• Label: 1.113.ap
• 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:	$1 - 15 x + 113 x^{2}$
Frobenius angles:	$\pm0.250704227710$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-227}) \)
Galois group:	$C_2$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$99$	$12771$	$1444608$	$163072899$	$18424541619$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$99$	$12771$	$1444608$	$163072899$	$18424541619$	$2081951714304$	$235260526020003$	$26584441603020675$	$3004041935582417664$	$339456738993037487811$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which 0 are hyperelliptic):

• $y^2=x^3+42 x+13$
• $y^2=x^3+74 x+109$
• $y^2=x^3+56 x+55$
• $y^2=x^3+50 x+50$
• $y^2=x^3+62 x+62$

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 \(\Q(\sqrt{-227}) \).

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.p	$2$	(not in LMFDB)