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

• Label: 2.113.au_ix
• 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:	$1 - 20 x + 231 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.120832024790$, $\pm0.496208905776$
Angle rank:	$2$ (numerical)
Number field:	4.0.4050275600.1
Galois group:	$D_{4}$
Jacobians:	$88$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10721$	$163827601$	$2080627085924$	$26580065119783721$	$339458048999073786961$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12832$	$1441978$	$163020516$	$18424422894$	$2081956505158$	$235260577747198$	$26584441928755908$	$3004041940949732794$	$339456739058044942272$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 88 curves (of which all are hyperelliptic):

• $y^2=33 x^6+11 x^5+24 x^4+19 x^3+55 x^2+63 x+63$
• $y^2=81 x^6+17 x^5+14 x^4+40 x^3+73 x^2+102 x+58$
• $y^2=66 x^6+35 x^5+20 x^4+39 x^3+92 x^2+33 x+22$
• $y^2=88 x^6+72 x^5+100 x^4+26 x^3+95 x^2+50 x+92$
• $y^2=14 x^6+52 x^5+28 x^4+39 x^3+90 x^2+85 x+55$
• $y^2=37 x^6+15 x^5+81 x^4+24 x^3+60 x^2+87 x+30$
• $y^2=12 x^6+25 x^5+82 x^4+78 x^3+45 x^2+10 x+110$
• $y^2=111 x^6+52 x^5+84 x^4+93 x^3+69 x^2+5 x+88$
• $y^2=11 x^6+87 x^5+45 x^4+37 x^3+81 x^2+62 x+73$
• $y^2=43 x^6+53 x^5+106 x^4+90 x^3+106 x^2+62 x+89$
• $y^2=70 x^6+94 x^5+69 x^4+112 x^3+42 x^2+56 x+50$
• $y^2=42 x^6+111 x^5+18 x^4+21 x^3+92 x^2+24 x+108$
• $y^2=13 x^6+20 x^5+72 x^4+97 x^3+52 x^2+10 x+10$
• $y^2=9 x^6+52 x^5+96 x^4+81 x^3+7 x^2+72 x+10$
• $y^2=74 x^6+20 x^5+34 x^4+95 x^3+5 x^2+13 x+83$
• $y^2=58 x^6+92 x^5+65 x^4+109 x^3+79 x^2+60 x+26$
• $y^2=49 x^6+50 x^5+30 x^4+90 x^3+6 x^2+6 x+5$
• $y^2=94 x^6+7 x^5+92 x^4+81 x^3+53 x^2+19 x+51$
• $y^2=3 x^6+18 x^5+48 x^4+13 x^3+71 x^2+83 x+55$
• $y^2=83 x^6+50 x^5+80 x^4+62 x^3+48 x^2+110 x+107$
• and

• $y^2=76 x^6+70 x^5+15 x^4+71 x^3+20 x^2+18 x+21$
• $y^2=105 x^6+16 x^5+87 x^4+61 x^3+17 x^2+88 x+26$
• $y^2=38 x^6+45 x^5+90 x^4+42 x^3+67 x^2+53 x+23$
• $y^2=23 x^6+105 x^5+70 x^4+2 x^3+x^2+49 x+21$
• $y^2=23 x^6+44 x^5+77 x^4+25 x^3+71 x^2+64 x+25$
• $y^2=2 x^6+14 x^5+5 x^4+77 x^3+22 x^2+67 x+51$
• $y^2=61 x^6+50 x^5+25 x^4+99 x^3+54 x^2+13 x+14$
• $y^2=20 x^6+80 x^5+44 x^4+92 x^3+38 x^2+40 x+56$
• $y^2=57 x^6+80 x^5+41 x^4+94 x^3+14 x^2+14 x+17$
• $y^2=15 x^6+46 x^5+21 x^4+107 x^3+98 x^2+90 x+95$
• $y^2=108 x^6+111 x^5+8 x^4+60 x^3+104 x^2+27 x+58$
• $y^2=74 x^6+54 x^5+36 x^3+89 x^2+43 x+5$
• $y^2=110 x^6+87 x^5+73 x^4+54 x^3+26 x^2+22 x+5$
• $y^2=82 x^6+109 x^5+10 x^4+104 x^3+51 x^2+112 x+20$
• $y^2=55 x^6+19 x^5+27 x^4+96 x^3+57 x^2+25 x+99$
• $y^2=51 x^6+36 x^5+98 x^4+31 x^3+71 x^2+4 x+106$
• $y^2=20 x^6+100 x^5+14 x^4+31 x^3+83 x^2+33 x+101$
• $y^2=34 x^6+105 x^5+79 x^4+16 x^3+80 x^2+95 x+62$
• $y^2=48 x^6+83 x^5+70 x^4+3 x^3+43 x^2+6 x+47$
• $y^2=72 x^6+25 x^4+33 x^3+94 x^2+55 x+81$
• $y^2=68 x^6+72 x^5+55 x^4+105 x^3+110 x^2+9 x+56$
• $y^2=101 x^6+20 x^5+73 x^4+49 x^3+83 x^2+48 x+54$
• $y^2=61 x^6+94 x^5+58 x^4+96 x^3+79 x^2+34 x+37$
• $y^2=20 x^6+52 x^5+80 x^4+72 x^3+107 x^2+18 x+63$
• $y^2=12 x^6+71 x^5+29 x^4+51 x^3+54 x^2+36 x+66$
• $y^2=24 x^6+82 x^5+61 x^4+46 x^3+74 x^2+49 x+30$
• $y^2=93 x^6+71 x^5+75 x^4+103 x^3+86 x^2+104 x+88$
• $y^2=65 x^6+31 x^5+3 x^4+75 x^3+40 x^2+15 x+29$
• $y^2=25 x^6+53 x^5+31 x^4+10 x^3+106 x^2+70 x+81$
• $y^2=55 x^6+3 x^5+106 x^4+30 x^3+50 x^2+24 x+46$
• $y^2=91 x^6+60 x^5+93 x^4+17 x^3+53 x^2+x+3$
• $y^2=49 x^6+78 x^5+64 x^4+49 x^3+38 x^2+39 x+37$
• $y^2=73 x^6+82 x^5+69 x^4+29 x^3+34 x^2+87 x+75$
• $y^2=49 x^6+74 x^5+79 x^4+56 x^3+12 x^2+22 x+21$
• $y^2=88 x^6+11 x^5+9 x^4+15 x^3+52 x^2+58 x+34$
• $y^2=21 x^6+64 x^5+86 x^4+60 x^3+24 x^2+105 x+42$
• $y^2=95 x^6+108 x^5+63 x^4+107 x^3+82 x^2+59 x+83$
• $y^2=59 x^6+46 x^5+73 x^4+104 x^3+34 x^2+7 x+58$
• $y^2=53 x^6+62 x^5+108 x^4+39 x^3+59 x^2+59 x+68$
• $y^2=4 x^6+37 x^5+2 x^4+88 x^3+48 x^2+37 x+5$
• $y^2=46 x^6+52 x^5+66 x^4+31 x^3+62 x^2+94 x+54$
• $y^2=69 x^6+49 x^5+32 x^4+81 x^3+77 x^2+96 x+87$
• $y^2=87 x^6+111 x^5+10 x^4+16 x^3+63 x^2+78 x+70$
• $y^2=42 x^6+70 x^5+4 x^4+95 x^3+87 x^2+37 x+11$
• $y^2=46 x^6+2 x^5+31 x^4+57 x^3+103 x^2+2 x+11$
• $y^2=80 x^6+63 x^5+88 x^4+91 x^3+82 x^2+45 x+12$
• $y^2=x^6+60 x^5+24 x^4+4 x^3+92 x^2+84 x+21$
• $y^2=39 x^6+34 x^5+70 x^4+95 x^3+103 x^2+52 x+95$
• $y^2=18 x^6+21 x^5+14 x^4+81 x^3+41 x^2+48 x+111$
• $y^2=5 x^6+57 x^5+20 x^4+111 x^3+105 x^2+13 x+75$
• $y^2=63 x^6+102 x^5+19 x^4+54 x^3+36 x^2+5 x+85$
• $y^2=40 x^6+40 x^5+103 x^4+27 x^3+29 x^2+89 x+38$
• $y^2=89 x^6+27 x^5+85 x^4+7 x^3+32 x^2+49 x+59$
• $y^2=29 x^6+30 x^5+22 x^4+92 x^3+22 x^2+73 x+86$
• $y^2=23 x^6+33 x^5+28 x^4+47 x^3+76 x^2+91 x+92$
• $y^2=108 x^6+71 x^5+41 x^4+24 x^3+21 x^2+95 x+96$
• $y^2=57 x^6+42 x^5+75 x^4+14 x^3+x^2+79 x+109$
• $y^2=84 x^6+59 x^5+68 x^4+5 x^3+2 x^2+31 x+87$
• $y^2=89 x^6+89 x^5+88 x^4+62 x^3+3 x^2+94 x+35$
• $y^2=47 x^6+95 x^5+83 x^4+107 x^3+55 x^2+89 x+12$
• $y^2=19 x^6+32 x^5+67 x^4+44 x^3+5 x^2+38 x+73$
• $y^2=87 x^6+x^5+16 x^4+22 x^3+91 x^2+99 x+77$
• $y^2=68 x^6+62 x^5+18 x^4+55 x^3+86 x^2+9 x+56$
• $y^2=103 x^6+8 x^5+87 x^4+34 x^3+35 x^2+75 x+63$
• $y^2=40 x^6+74 x^5+102 x^4+99 x^3+16 x^2+111 x+79$
• $y^2=19 x^6+59 x^5+59 x^4+68 x^3+58 x^2+18 x+8$
• $y^2=33 x^6+24 x^5+x^4+105 x^3+63 x^2+67 x+11$
• $y^2=87 x^6+86 x^5+24 x^4+39 x^3+79 x^2+9 x+20$

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 4.0.4050275600.1.

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.u_ix	$2$	(not in LMFDB)