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

• Label: 2.113.aw_kb
• 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:	$1 - 22 x + 261 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0973556696352$, $\pm0.474124061097$
Angle rank:	$2$ (numerical)
Number field:	4.0.2177500736.1
Galois group:	$D_{4}$
Jacobians:	$46$
Isomorphism classes:	46

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10523$	$163516897$	$2080684041164$	$26579079185632169$	$339454553865309459523$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12808$	$1442018$	$163014468$	$18424233192$	$2081955055798$	$235260581132312$	$26584441920036036$	$3004041938875964354$	$339456739054273113768$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 46 curves (of which all are hyperelliptic):

• $y^2=35 x^6+31 x^5+111 x^4+107 x^3+65 x^2+84 x+30$
• $y^2=77 x^6+46 x^5+4 x^4+6 x^3+82 x^2+110 x+3$
• $y^2=43 x^6+62 x^5+60 x^4+50 x^3+x^2+70 x+34$
• $y^2=104 x^6+65 x^5+105 x^4+40 x^3+107 x^2+13 x+38$
• $y^2=96 x^6+x^5+12 x^4+37 x^3+6 x^2+14 x+62$
• $y^2=101 x^6+27 x^5+34 x^4+93 x^3+98 x^2+34 x+38$
• $y^2=18 x^6+73 x^5+55 x^4+107 x^3+25 x^2+101 x+84$
• $y^2=40 x^6+97 x^5+43 x^4+35 x^3+56 x^2+78 x+30$
• $y^2=43 x^6+13 x^5+102 x^4+50 x^3+53 x^2+106 x+42$
• $y^2=86 x^6+92 x^5+35 x^4+15 x^3+17 x^2+83 x+72$
• $y^2=47 x^6+24 x^5+105 x^4+39 x^3+26 x^2+74 x+29$
• $y^2=112 x^6+90 x^5+24 x^4+101 x^3+36 x^2+32 x+68$
• $y^2=9 x^6+23 x^5+68 x^4+87 x^3+86 x^2+96 x+38$
• $y^2=110 x^6+80 x^5+46 x^4+76 x^3+74 x^2+71 x+47$
• $y^2=49 x^6+18 x^5+x^4+14 x^3+55 x^2+87 x+18$
• $y^2=65 x^6+106 x^5+13 x^4+26 x^3+42 x^2+86 x+51$
• $y^2=70 x^6+40 x^5+63 x^4+35 x^3+7 x^2+109 x+68$
• $y^2=110 x^6+32 x^5+53 x^4+33 x^3+20 x^2+8 x+23$
• $y^2=112 x^6+57 x^5+15 x^4+105 x^3+73 x^2+69 x+54$
• $y^2=19 x^6+8 x^5+108 x^4+94 x^3+107 x^2+17 x+63$
• and

• $y^2=34 x^6+98 x^5+4 x^4+55 x^2+20 x+7$
• $y^2=44 x^6+9 x^5+90 x^4+78 x^3+89 x^2+59 x+1$
• $y^2=101 x^6+103 x^5+57 x^4+37 x^3+32 x^2+45 x+110$
• $y^2=90 x^6+76 x^5+96 x^4+81 x^3+52 x^2+35 x+61$
• $y^2=6 x^6+89 x^5+89 x^4+42 x^3+52 x^2+85 x+107$
• $y^2=42 x^6+90 x^5+2 x^4+9 x^3+107 x^2+68 x+69$
• $y^2=12 x^6+84 x^5+2 x^4+x^3+100 x^2+38 x+48$
• $y^2=55 x^6+103 x^5+74 x^4+25 x^3+46 x^2+88 x+99$
• $y^2=40 x^6+5 x^5+56 x^4+52 x^3+37 x^2+70 x+70$
• $y^2=10 x^6+30 x^5+18 x^4+78 x^3+48 x^2+21 x+58$
• $y^2=108 x^6+22 x^5+23 x^4+97 x^3+66 x^2+60 x+28$
• $y^2=65 x^6+66 x^5+103 x^4+79 x^3+27 x^2+68 x+72$
• $y^2=84 x^6+97 x^5+83 x^4+93 x^3+109 x^2+10 x+39$
• $y^2=48 x^6+102 x^5+38 x^4+34 x^3+102 x^2+56 x+20$
• $y^2=17 x^6+94 x^5+48 x^4+84 x^3+73 x^2+58 x+111$
• $y^2=92 x^6+48 x^5+112 x^4+40 x^3+23 x^2+33 x+29$
• $y^2=46 x^6+2 x^5+86 x^4+18 x^3+24 x^2+8 x+36$
• $y^2=51 x^6+53 x^5+52 x^4+31 x^3+36 x^2+72 x+33$
• $y^2=4 x^6+57 x^5+33 x^4+37 x^3+76 x^2+66 x+109$
• $y^2=90 x^6+35 x^5+38 x^4+80 x^3+106 x^2+81 x+6$
• $y^2=56 x^6+102 x^5+85 x^4+15 x^3+100 x^2+104 x+105$
• $y^2=107 x^6+65 x^5+38 x^4+23 x^3+103 x^2+90 x+55$
• $y^2=31 x^6+101 x^5+68 x^4+82 x^3+58 x^2+9 x+14$
• $y^2=60 x^6+52 x^5+46 x^4+101 x^3+5 x^2+61 x+72$
• $y^2=44 x^6+61 x^4+98 x^3+17 x^2+59 x+7$
• $y^2=71 x^6+13 x^5+35 x^4+42 x^3+26 x^2+8 x+24$

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 4.0.2177500736.1.

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_kb	$2$	(not in LMFDB)