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

• Label: 2.113.aw_jj
• 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:	$1 - 22 x + 243 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0243649366610$, $\pm0.487990160899$
Angle rank:	$2$ (numerical)
Number field:	4.0.12903488.1
Galois group:	$D_{4}$
Jacobians:	$42$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10505$	$163048105$	$2078970090560$	$26576356046887625$	$339451161216780990025$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12772$	$1440830$	$162997764$	$18424049052$	$2081951978014$	$235260529675676$	$26584441350870276$	$3004041934153767710$	$339456738999908584932$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=56 x^6+58 x^5+5 x^4+52 x^3+73 x^2+111 x+3$
• $y^2=50 x^6+111 x^5+x^4+37 x^3+89 x^2+23 x+49$
• $y^2=86 x^6+19 x^5+57 x^4+73 x^3+82 x^2+45 x+68$
• $y^2=78 x^6+110 x^5+91 x^4+61 x^3+98 x^2+32 x+47$
• $y^2=57 x^6+92 x^5+98 x^4+2 x^3+9 x^2+81 x+29$
• $y^2=7 x^6+78 x^5+78 x^4+85 x^3+25 x^2+50 x+80$
• $y^2=31 x^6+75 x^5+73 x^4+19 x^3+61 x^2+76 x+58$
• $y^2=92 x^6+35 x^5+58 x^4+11 x^3+68 x^2+43 x+56$
• $y^2=45 x^6+50 x^5+94 x^4+80 x^3+79 x^2+43 x+58$
• $y^2=95 x^6+108 x^5+46 x^4+85 x^3+93 x^2+93 x+60$
• $y^2=12 x^6+76 x^5+72 x^4+26 x^3+76 x^2+99 x+80$
• $y^2=55 x^6+63 x^5+101 x^4+112 x^3+38 x^2+59 x+21$
• $y^2=63 x^6+99 x^5+83 x^4+17 x^3+11 x^2+101 x+57$
• $y^2=62 x^6+53 x^5+65 x^4+15 x^2+2 x+18$
• $y^2=65 x^6+90 x^5+47 x^4+104 x^3+16 x^2+16 x+102$
• $y^2=4 x^6+84 x^5+111 x^4+4 x^3+60 x^2+54 x+28$
• $y^2=83 x^6+41 x^5+30 x^4+3 x^3+94 x^2+45 x+74$
• $y^2=5 x^6+27 x^5+80 x^4+39 x^3+112 x^2+3 x+108$
• $y^2=74 x^6+109 x^5+19 x^4+8 x^3+76 x^2+x+107$
• $y^2=9 x^6+28 x^4+78 x^3+45 x^2+100 x+16$
• and

• $y^2=103 x^6+110 x^5+58 x^4+53 x^3+53 x^2+25 x+43$
• $y^2=93 x^6+x^5+43 x^4+96 x^3+24 x^2+111 x+43$
• $y^2=66 x^6+46 x^5+53 x^4+52 x^3+49 x^2+7 x+12$
• $y^2=30 x^6+77 x^5+83 x^4+2 x^3+105 x^2+30 x+78$
• $y^2=33 x^6+50 x^5+31 x^4+17 x^3+4 x^2+70 x+38$
• $y^2=46 x^6+27 x^5+30 x^4+21 x^3+10 x^2+23 x+110$
• $y^2=5 x^6+44 x^5+21 x^4+24 x^3+2 x^2+98 x+37$
• $y^2=82 x^6+90 x^5+45 x^4+34 x^3+107 x^2+34 x+79$
• $y^2=2 x^6+39 x^5+48 x^4+74 x^3+33 x^2+46 x+36$
• $y^2=40 x^6+80 x^5+26 x^4+75 x^3+46 x^2+40 x+65$
• $y^2=53 x^6+63 x^5+49 x^4+85 x^3+53 x^2+14 x+26$
• $y^2=92 x^6+88 x^5+85 x^4+69 x^3+17 x^2+65 x+107$
• $y^2=50 x^6+22 x^5+17 x^4+39 x^3+75 x^2+27 x+78$
• $y^2=74 x^6+38 x^5+7 x^4+3 x^3+16 x^2+29 x+30$
• $y^2=22 x^6+83 x^5+41 x^4+27 x^3+100 x^2+38 x+39$
• $y^2=29 x^6+106 x^5+47 x^4+102 x^3+109 x^2+53 x+45$
• $y^2=47 x^6+50 x^5+108 x^4+19 x^3+x^2+109 x+76$
• $y^2=22 x^6+9 x^5+3 x^4+84 x^3+55 x^2+82 x+63$
• $y^2=51 x^6+44 x^5+85 x^4+32 x^3+44 x^2+77 x+57$
• $y^2=35 x^6+25 x^5+38 x^4+53 x^3+86 x^2+71 x+81$
• $y^2=99 x^6+28 x^5+43 x^4+78 x^3+101 x^2+94 x+49$
• $y^2=2 x^6+107 x^5+30 x^4+102 x^3+21 x^2+91 x+72$

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 4.0.12903488.1.

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.w_jj	$2$	(not in LMFDB)