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

• Label: 2.113.abg_ro
• 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:	$1 - 32 x + 456 x^{2} - 3616 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0392315139262$, $\pm0.328630858736$
Angle rank:	$2$ (numerical)
Number field:	4.0.24617216.1
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9578$	$161619172$	$2082180125834$	$26583065167088144$	$339450483029715439498$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$82$	$12658$	$1443058$	$163038918$	$18424012242$	$2081946746098$	$235260510095602$	$26584441877660286$	$3004041939876373714$	$339456739002913716018$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=78 x^6+88 x^5+32 x^4+25 x^3+30 x^2+29 x+92$
• $y^2=86 x^6+45 x^5+16 x^4+16 x^3+100 x^2+74 x+91$
• $y^2=21 x^6+81 x^5+48 x^4+57 x^3+108 x^2+70 x+8$
• $y^2=21 x^6+48 x^5+53 x^4+x^3+66 x^2+106 x+11$
• $y^2=16 x^6+35 x^5+75 x^4+94 x^3+109 x^2+7 x+87$
• $y^2=88 x^6+107 x^4+46 x^3+98 x^2+69 x+1$
• $y^2=29 x^6+19 x^5+82 x^4+61 x^3+74 x^2+98 x+10$
• $y^2=69 x^6+64 x^5+87 x^4+32 x^3+21 x^2+60 x+73$
• $y^2=88 x^6+59 x^5+89 x^4+18 x^3+56 x^2+10 x+78$
• $y^2=7 x^6+12 x^5+102 x^4+99 x^3+2 x^2+62 x+9$
• $y^2=57 x^6+64 x^5+33 x^4+52 x^3+98 x^2+110 x+27$
• $y^2=39 x^6+69 x^5+59 x^4+72 x^3+38 x^2+109 x+20$
• $y^2=36 x^6+28 x^5+84 x^4+50 x^3+85 x^2+106 x+27$
• $y^2=49 x^6+10 x^5+30 x^4+47 x^3+32 x^2+28 x+110$
• $y^2=68 x^6+101 x^5+27 x^4+87 x^2+46 x+109$
• $y^2=39 x^6+106 x^5+86 x^4+21 x^3+68 x^2+56 x+10$

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 4.0.24617216.1.

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.bg_ro	$2$	(not in LMFDB)