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

• Label: 2.113.az_mw
• 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:	$1 - 25 x + 334 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.132447889921$, $\pm0.415872641312$
Angle rank:	$2$ (numerical)
Number field:	4.0.1158443900.1
Galois group:	$D_{4}$
Jacobians:	$80$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10254$	$163592316$	$2083324088376$	$26582785500966336$	$339454332313272304014$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12813$	$1443848$	$163037201$	$18424221169$	$2081954015442$	$235260607408993$	$26584442418112993$	$3004041938443301624$	$339456738979165585053$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 80 curves (of which all are hyperelliptic):

• $y^2=92 x^6+61 x^5+80 x^4+106 x^3+3 x^2+109 x+95$
• $y^2=30 x^6+86 x^5+25 x^4+69 x^3+16 x^2+103 x+104$
• $y^2=42 x^6+23 x^5+9 x^4+87 x^3+91 x^2+91 x+49$
• $y^2=8 x^6+97 x^5+104 x^4+26 x^3+90 x^2+95 x+19$
• $y^2=76 x^6+97 x^5+42 x^4+63 x^3+33 x^2+88 x+62$
• $y^2=40 x^6+43 x^5+13 x^4+54 x^3+85 x^2+34 x+38$
• $y^2=22 x^6+9 x^5+19 x^4+72 x^3+111 x^2+91 x+32$
• $y^2=39 x^6+87 x^5+22 x^4+71 x^3+15 x^2+112 x+9$
• $y^2=73 x^6+107 x^5+96 x^4+14 x^3+89 x^2+107 x+25$
• $y^2=89 x^6+71 x^5+83 x^4+12 x^3+22 x^2+18 x+103$
• $y^2=3 x^6+16 x^5+32 x^4+86 x^3+70 x^2+22 x+70$
• $y^2=33 x^6+81 x^5+85 x^4+72 x^3+14 x^2+71 x+45$
• $y^2=45 x^6+18 x^5+54 x^4+26 x^3+6 x^2+91 x+96$
• $y^2=82 x^6+19 x^5+54 x^4+81 x^3+6 x^2+79 x+59$
• $y^2=78 x^6+54 x^5+5 x^4+99 x^3+53 x^2+50 x+84$
• $y^2=106 x^6+102 x^5+35 x^4+11 x^3+41 x^2+33$
• $y^2=84 x^6+28 x^5+6 x^4+52 x^3+34 x^2+4 x+45$
• $y^2=80 x^6+68 x^5+110 x^4+44 x^3+68 x^2+95 x+35$
• $y^2=106 x^6+4 x^5+104 x^4+70 x^3+84 x^2+35 x+43$
• $y^2=28 x^6+29 x^5+10 x^4+106 x^3+29 x^2+2 x+46$
• and

• $y^2=17 x^6+39 x^5+51 x^4+13 x^3+19 x^2+17 x+75$
• $y^2=3 x^6+93 x^5+69 x^4+37 x^3+112 x^2+45 x+49$
• $y^2=93 x^6+55 x^5+85 x^4+73 x^3+29 x^2+10 x+10$
• $y^2=65 x^6+98 x^5+112 x^4+98 x^3+15 x^2+106 x+21$
• $y^2=25 x^6+27 x^5+4 x^4+94 x^3+84 x^2+54 x+89$
• $y^2=39 x^6+3 x^5+96 x^4+32 x^3+89 x^2+47 x+49$
• $y^2=61 x^6+24 x^5+40 x^4+8 x^3+18 x^2+75 x+77$
• $y^2=79 x^6+107 x^5+73 x^4+95 x^3+102 x^2+17 x+90$
• $y^2=43 x^6+89 x^5+22 x^4+4 x^3+14 x^2+74 x+99$
• $y^2=19 x^6+36 x^5+72 x^4+7 x^3+68 x^2+27 x+81$
• $y^2=107 x^6+46 x^5+95 x^4+33 x^3+108 x^2+95 x+6$
• $y^2=38 x^6+78 x^5+24 x^4+55 x^3+63 x^2+41 x+63$
• $y^2=22 x^6+16 x^5+38 x^4+21 x^3+16 x^2+106 x+8$
• $y^2=111 x^6+40 x^5+66 x^4+70 x^3+109 x^2+78 x+86$
• $y^2=53 x^6+31 x^5+88 x^4+21 x^3+74 x^2+62 x+111$
• $y^2=92 x^6+56 x^5+50 x^4+26 x^3+69 x^2+7 x+34$
• $y^2=80 x^6+70 x^5+x^4+87 x^3+111 x^2+6 x+3$
• $y^2=73 x^6+88 x^5+95 x^4+67 x^3+32 x^2+100 x+93$
• $y^2=76 x^6+100 x^5+57 x^4+59 x^3+105 x^2+95 x+85$
• $y^2=17 x^6+94 x^5+48 x^4+5 x^3+32 x^2+93 x+62$
• $y^2=57 x^6+57 x^4+38 x^3+65 x^2+37 x+45$
• $y^2=6 x^6+78 x^5+3 x^4+75 x^3+33 x^2+87 x+88$
• $y^2=59 x^6+21 x^5+67 x^4+102 x^3+51 x^2+2 x+55$
• $y^2=19 x^6+82 x^5+30 x^4+77 x^3+69 x^2+63 x+3$
• $y^2=43 x^6+39 x^5+103 x^4+26 x^3+107 x^2+53 x+58$
• $y^2=72 x^6+105 x^5+3 x^4+74 x^3+69 x^2+89 x+76$
• $y^2=99 x^6+112 x^5+112 x^4+60 x^3+49 x^2+34 x+66$
• $y^2=67 x^6+17 x^5+58 x^4+15 x^3+24 x^2+37 x+23$
• $y^2=7 x^6+69 x^5+71 x^4+94 x^3+14 x^2+74 x+65$
• $y^2=44 x^6+74 x^5+42 x^4+19 x^3+68 x^2+109 x+20$
• $y^2=54 x^6+70 x^5+66 x^4+63 x^3+61 x^2+17 x+53$
• $y^2=109 x^6+21 x^5+5 x^4+65 x^3+22 x^2+21 x+12$
• $y^2=11 x^6+11 x^5+76 x^4+2 x^3+54 x^2+21 x+107$
• $y^2=40 x^6+75 x^5+40 x^4+83 x^3+112 x^2+35 x+35$
• $y^2=87 x^6+86 x^5+58 x^4+83 x^3+24 x^2+76 x+86$
• $y^2=58 x^6+54 x^5+111 x^4+108 x^3+34 x^2+87 x+47$
• $y^2=79 x^6+59 x^5+72 x^4+73 x^3+67 x^2+76 x+97$
• $y^2=17 x^6+x^5+23 x^4+82 x^3+112 x^2+10 x+63$
• $y^2=89 x^6+35 x^5+97 x^4+105 x^3+58 x^2+39 x+75$
• $y^2=96 x^6+65 x^5+x^4+65 x^3+40 x^2+47 x+80$
• $y^2=104 x^6+64 x^5+25 x^4+92 x^3+26 x^2+94 x+39$
• $y^2=2 x^5+112 x^4+63 x^3+13 x^2+14 x+43$
• $y^2=93 x^6+35 x^5+59 x^4+x^3+53 x+15$
• $y^2=90 x^6+45 x^5+19 x^4+66 x^3+64 x^2+97 x+89$
• $y^2=104 x^6+33 x^5+33 x^4+26 x^3+27 x^2+80 x+30$
• $y^2=90 x^6+104 x^5+49 x^4+61 x^3+69 x^2+25 x+6$
• $y^2=16 x^6+x^5+17 x^4+30 x^3+84 x^2+103 x+105$
• $y^2=36 x^6+66 x^5+13 x^4+36 x^3+28 x^2+39 x+101$
• $y^2=80 x^6+8 x^5+51 x^4+9 x^3+8 x^2+5 x+64$
• $y^2=3 x^6+2 x^5+63 x^4+44 x^3+12 x^2+27 x+29$
• $y^2=101 x^6+36 x^5+x^4+110 x^3+72 x^2+71 x+37$
• $y^2=25 x^6+53 x^5+94 x^4+76 x^3+5 x^2+18 x+96$
• $y^2=100 x^6+46 x^5+60 x^4+35 x^3+109 x^2+107 x+112$
• $y^2=65 x^6+42 x^5+12 x^4+84 x^3+86 x^2+5 x+110$
• $y^2=38 x^6+80 x^5+62 x^4+96 x^3+70 x^2+26 x+16$
• $y^2=109 x^6+29 x^5+98 x^4+54 x^3+81 x^2+22 x+5$
• $y^2=27 x^6+46 x^5+61 x^4+15 x^3+39 x^2+9 x+39$
• $y^2=99 x^6+56 x^5+68 x^4+48 x^3+79 x^2+65 x+11$
• $y^2=79 x^6+40 x^5+108 x^4+6 x^3+95 x^2+52 x+34$
• $y^2=18 x^6+95 x^5+77 x^4+76 x^3+5 x^2+53 x+21$

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 4.0.1158443900.1.

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.z_mw	$2$	(not in LMFDB)