Abelian variety isogeny class 2.113.abn_xh over $\F_{113}$

• Label: 2.113.abn_xh
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 39 x + 605 x^{2} - 4407 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0784394555333$, $\pm0.167562406750$
Angle rank:	$2$ (numerical)
Number field:	4.0.76725.1
Galois group:	$D_{4}$
Jacobians:	$4$

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:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8929$	$159123709$	$2079422316409$	$26584264839081141$	$339459443628842308864$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$75$	$12459$	$1441143$	$163046275$	$18424498590$	$2081954372163$	$235260579014991$	$26584442212881379$	$3004041939986110779$	$339456739001621333214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which all are hyperelliptic):

• $y^2=95 x^6+58 x^5+98 x^4+6 x^3+105 x^2+35 x+17$
• $y^2=8 x^6+10 x^5+40 x^4+38 x^3+74 x^2+64 x+12$
• $y^2=83 x^6+94 x^5+32 x^4+98 x^3+80 x^2+47 x+93$
• $y^2=14 x^6+50 x^5+32 x^4+110 x^3+7 x^2+111 x+101$

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 4.0.76725.1.

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
2.113.bn_xh	$2$	(not in LMFDB)