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

• Label: 2.113.abb_pk
• 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:	$1 - 27 x + 400 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.220212599309$, $\pm0.333375292598$
Angle rank:	$2$ (numerical)
Number field:	4.0.16979688.2
Galois group:	$D_{4}$
Jacobians:	$90$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10092$	$163974816$	$2087099917488$	$26590398189388416$	$339458987004459526092$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12841$	$1446462$	$163083889$	$18424473807$	$2081950403326$	$235260528744111$	$26584441853507233$	$3004041937989860190$	$339456738980938682521$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 90 curves (of which all are hyperelliptic):

• $y^2=17 x^6+90 x^4+60 x^3+9 x^2+79 x+42$
• $y^2=10 x^6+79 x^5+88 x^4+72 x^3+74 x^2+85 x+5$
• $y^2=45 x^6+34 x^5+77 x^4+29 x^3+82 x^2+24 x+71$
• $y^2=21 x^6+57 x^5+84 x^4+86 x^3+100 x^2+14 x+5$
• $y^2=12 x^6+75 x^5+106 x^3+60 x^2+82 x+70$
• $y^2=27 x^6+42 x^5+36 x^4+76 x^3+28 x^2+59 x+103$
• $y^2=66 x^6+103 x^5+32 x^4+59 x^3+73 x^2+90 x+89$
• $y^2=109 x^6+68 x^5+2 x^4+35 x^3+36 x^2+45 x+37$
• $y^2=10 x^5+62 x^4+101 x^3+13 x^2+101 x+79$
• $y^2=20 x^6+38 x^5+79 x^4+67 x^3+6 x^2+109 x+63$
• $y^2=74 x^6+74 x^5+104 x^4+24 x^3+18 x^2+73 x+67$
• $y^2=11 x^6+65 x^5+95 x^4+107 x^3+111 x^2+28 x+40$
• $y^2=21 x^6+105 x^5+61 x^4+71 x^3+34 x^2+84 x+2$
• $y^2=26 x^6+77 x^5+7 x^4+60 x^3+37 x^2+65 x+27$
• $y^2=26 x^6+86 x^5+79 x^4+4 x^3+91 x^2+26 x+27$
• $y^2=22 x^6+43 x^5+34 x^4+110 x^3+13 x^2+19 x+48$
• $y^2=28 x^6+26 x^5+21 x^4+12 x^3+9 x^2+66 x+2$
• $y^2=11 x^6+78 x^5+97 x^4+47 x^3+102 x^2+21 x+30$
• $y^2=71 x^6+21 x^5+54 x^4+90 x^3+97 x^2+70 x+78$
• $y^2=91 x^6+24 x^5+32 x^4+45 x^3+16 x^2+6 x+84$
• and

• $y^2=32 x^5+5 x^4+43 x^3+103 x^2+108 x+46$
• $y^2=44 x^6+95 x^5+86 x^4+82 x^3+98 x^2+22 x+77$
• $y^2=58 x^6+36 x^5+86 x^4+89 x^3+12 x^2+108 x+6$
• $y^2=29 x^6+83 x^5+70 x^4+33 x^3+85 x^2+76 x+21$
• $y^2=88 x^6+72 x^5+78 x^4+77 x^3+20 x^2+26 x+94$
• $y^2=103 x^6+12 x^5+71 x^4+77 x^3+56 x^2+56 x+18$
• $y^2=25 x^6+103 x^5+107 x^4+107 x^3+62 x^2+97 x+40$
• $y^2=77 x^6+90 x^5+26 x^4+104 x^3+3 x^2+78 x+91$
• $y^2=73 x^6+88 x^5+98 x^4+106 x^3+93 x^2+77 x+67$
• $y^2=26 x^6+43 x^5+108 x^4+106 x^3+97 x^2+107 x+107$
• $y^2=69 x^6+58 x^5+83 x^4+73 x^3+103 x^2+70 x+40$
• $y^2=58 x^6+2 x^5+57 x^4+5 x^3+44 x^2+x+94$
• $y^2=5 x^6+66 x^5+45 x^4+11 x^3+47 x^2+57 x+66$
• $y^2=83 x^6+12 x^5+26 x^4+39 x^3+50 x^2+29 x+3$
• $y^2=65 x^6+112 x^5+37 x^4+29 x^3+62 x^2+61 x$
• $y^2=55 x^6+29 x^5+32 x^4+34 x^3+63 x^2+44 x+22$
• $y^2=14 x^6+18 x^5+75 x^4+66 x^3+38 x^2+x+52$
• $y^2=103 x^6+90 x^5+85 x^4+28 x^3+68 x^2+73 x+35$
• $y^2=59 x^6+17 x^5+10 x^4+106 x^3+61 x^2+5 x+35$
• $y^2=80 x^6+97 x^5+24 x^4+35 x^3+88 x+27$
• $y^2=112 x^6+84 x^5+46 x^4+57 x^3+89 x^2+70 x+78$
• $y^2=89 x^6+2 x^5+112 x^4+32 x^3+24 x^2+100 x+111$
• $y^2=47 x^6+52 x^5+49 x^4+102 x^3+100 x^2+35 x+5$
• $y^2=12 x^6+50 x^5+41 x^4+67 x^3+33 x^2+88 x+81$
• $y^2=67 x^6+16 x^5+27 x^4+22 x^3+39 x^2+108 x+30$
• $y^2=33 x^6+56 x^5+66 x^4+75 x^3+42 x^2+35 x+95$
• $y^2=112 x^6+27 x^5+47 x^4+91 x^3+98 x^2+10 x+106$
• $y^2=95 x^6+27 x^5+66 x^4+97 x^3+101 x^2+17 x+49$
• $y^2=47 x^6+22 x^5+33 x^4+106 x^3+83 x^2+28 x+23$
• $y^2=53 x^6+98 x^5+93 x^4+57 x^3+78 x^2+86 x+96$
• $y^2=81 x^6+93 x^5+42 x^4+89 x^3+108 x^2+32 x+49$
• $y^2=104 x^6+85 x^5+57 x^4+77 x^3+50 x^2+81 x+79$
• $y^2=56 x^6+83 x^5+32 x^4+35 x^3+32 x^2+27 x+64$
• $y^2=9 x^6+84 x^5+40 x^4+78 x^3+65 x^2+106 x+59$
• $y^2=77 x^6+106 x^5+101 x^4+26 x^3+55 x^2+80 x+75$
• $y^2=62 x^6+79 x^5+2 x^4+68 x^3+28 x^2+55 x$
• $y^2=95 x^6+2 x^5+42 x^4+43 x^3+89 x^2+105 x+10$
• $y^2=87 x^6+18 x^5+17 x^4+88 x^3+33 x^2+10 x+89$
• $y^2=27 x^6+102 x^5+58 x^4+106 x^3+3 x^2+40 x+93$
• $y^2=91 x^6+100 x^5+108 x^4+36 x^3+40 x^2+75 x+107$
• $y^2=67 x^6+98 x^5+6 x^4+58 x^3+54 x^2+62 x+18$
• $y^2=55 x^6+99 x^5+41 x^4+52 x^3+38 x^2+66 x+111$
• $y^2=95 x^6+100 x^5+34 x^4+90 x^3+90 x^2+11 x+14$
• $y^2=103 x^6+81 x^5+33 x^4+112 x^3+20 x^2+109 x+40$
• $y^2=23 x^6+69 x^5+44 x^4+98 x^3+31 x^2+8 x+42$
• $y^2=51 x^6+16 x^5+86 x^4+103 x^3+46 x^2+15 x+68$
• $y^2=82 x^6+15 x^5+108 x^4+75 x^3+75 x^2+53 x+96$
• $y^2=14 x^6+62 x^5+13 x^4+39 x^3+87 x^2+15 x+78$
• $y^2=107 x^6+81 x^5+24 x^4+21 x^3+66 x^2+62 x+100$
• $y^2=55 x^6+83 x^5+53 x^4+30 x^3+69 x^2+80 x+91$
• $y^2=15 x^6+32 x^5+91 x^4+3 x^3+78 x^2+47 x+108$
• $y^2=86 x^6+41 x^5+93 x^4+66 x^3+43 x^2+48 x+41$
• $y^2=90 x^6+54 x^5+53 x^4+16 x^3+55 x^2+45 x+31$
• $y^2=27 x^6+110 x^5+30 x^4+10 x^3+79 x^2+56 x+46$
• $y^2=95 x^6+100 x^5+8 x^4+33 x^3+99 x^2+87 x+17$
• $y^2=49 x^6+62 x^5+91 x^4+78 x^3+13 x^2+76 x+14$
• $y^2=78 x^6+20 x^5+99 x^4+73 x^3+100 x^2+9 x+32$
• $y^2=104 x^6+34 x^5+103 x^4+80 x^3+110 x^2+54 x+43$
• $y^2=27 x^6+64 x^5+86 x^4+7 x^3+64 x^2+75 x+23$
• $y^2=52 x^6+69 x^5+59 x^4+84 x^3+76 x^2+93 x+107$
• $y^2=100 x^6+24 x^5+40 x^4+7 x^3+33 x^2+78 x+14$
• $y^2=51 x^6+12 x^5+11 x^4+30 x^3+31 x^2+93 x+38$
• $y^2=67 x^6+5 x^5+110 x^4+30 x^3+89 x^2+21 x+109$
• $y^2=10 x^6+71 x^5+29 x^4+8 x^3+58 x^2+47 x+29$
• $y^2=79 x^6+68 x^5+72 x^4+20 x^3+32 x^2+x+13$
• $y^2=10 x^6+74 x^5+73 x^4+70 x^3+40 x^2+54 x+76$
• $y^2=32 x^6+42 x^5+68 x^4+62 x^3+4 x^2+56 x+111$
• $y^2=6 x^6+49 x^5+47 x^4+22 x^3+45 x^2+56 x+92$
• $y^2=53 x^6+68 x^5+109 x^4+71 x^3+38 x^2+27 x+38$
• $y^2=94 x^6+95 x^5+59 x^4+69 x^3+100 x^2+19 x+5$

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 4.0.16979688.2.

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.bb_pk	$2$	(not in LMFDB)