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

• Label: 2.113.au_jf
• 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:	$1 - 20 x + 239 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.136783358378$, $\pm0.489927813143$
Angle rank:	$2$ (numerical)
Number field:	4.0.4290109200.1
Galois group:	$D_{4}$
Jacobians:	$96$
Isomorphism classes:	192

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10729$	$164035681$	$2081319611236$	$26580925880300041$	$339458682791843454889$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12848$	$1442458$	$163025796$	$18424457294$	$2081957026502$	$235260585187358$	$26584441925261188$	$3004041939603004954$	$339456739042105810928$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 96 curves (of which all are hyperelliptic):

• $y^2=3 x^6+86 x^5+4 x^4+39 x^3+106 x^2+96 x+109$
• $y^2=23 x^6+56 x^5+47 x^4+67 x^3+18 x^2+39 x+50$
• $y^2=90 x^6+17 x^5+31 x^4+7 x^3+54 x^2+60 x+21$
• $y^2=57 x^6+41 x^5+70 x^4+x^3+58 x^2+51 x+30$
• $y^2=24 x^6+29 x^5+53 x^4+49 x^3+19 x^2+41 x+37$
• $y^2=102 x^6+75 x^5+80 x^4+42 x^3+108 x^2+13 x+103$
• $y^2=28 x^6+3 x^5+50 x^4+28 x^3+95 x^2+4 x+30$
• $y^2=42 x^6+2 x^5+104 x^4+97 x^2+30 x+100$
• $y^2=73 x^6+22 x^5+93 x^4+7 x^3+12 x^2+10 x+2$
• $y^2=40 x^6+87 x^5+27 x^4+20 x^3+91 x^2+42 x+81$
• $y^2=67 x^6+31 x^5+22 x^4+102 x^3+18 x^2+41 x+42$
• $y^2=94 x^6+85 x^5+5 x^4+24 x^3+89 x^2+69 x+67$
• $y^2=99 x^6+64 x^5+41 x^4+52 x^3+15 x^2+4 x+82$
• $y^2=111 x^6+86 x^5+10 x^4+14 x^3+20 x^2+69 x+41$
• $y^2=29 x^6+69 x^5+8 x^4+53 x^3+111 x^2+100 x+12$
• $y^2=18 x^6+111 x^5+75 x^4+17 x^3+105 x^2+66 x+24$
• $y^2=50 x^6+88 x^5+96 x^4+53 x^3+99 x^2+9 x+109$
• $y^2=106 x^6+62 x^5+61 x^4+91 x^3+13 x^2+61 x+77$
• $y^2=21 x^6+90 x^5+69 x^4+82 x^3+32 x^2+22 x+57$
• $y^2=90 x^6+104 x^5+59 x^4+41 x^3+64 x^2+26 x+19$
• and

• $y^2=42 x^6+37 x^5+10 x^4+77 x^3+87 x^2+78 x+40$
• $y^2=18 x^6+101 x^5+2 x^4+58 x^3+103 x^2+14 x+41$
• $y^2=21 x^6+75 x^5+79 x^4+30 x^3+5 x^2+12 x+3$
• $y^2=71 x^6+55 x^5+74 x^4+35 x^3+3 x^2+8 x+112$
• $y^2=96 x^6+23 x^5+74 x^4+40 x^3+98 x^2+106 x+81$
• $y^2=30 x^6+84 x^5+15 x^4+104 x^3+7 x^2+89 x+80$
• $y^2=17 x^6+18 x^5+48 x^4+72 x^3+22 x^2+99 x+83$
• $y^2=65 x^6+81 x^5+2 x^4+71 x^3+4 x^2+49 x+107$
• $y^2=81 x^6+36 x^5+29 x^4+91 x^3+29 x^2+5 x+64$
• $y^2=42 x^6+38 x^5+24 x^4+34 x^3+34 x^2+42 x+68$
• $y^2=47 x^6+75 x^5+25 x^4+95 x^3+109 x^2+110 x+96$
• $y^2=103 x^6+8 x^5+63 x^4+28 x^3+93 x^2+68 x+81$
• $y^2=68 x^6+78 x^5+65 x^4+75 x^3+70 x^2+20 x+17$
• $y^2=74 x^6+20 x^5+58 x^4+60 x^3+79 x^2+2 x+77$
• $y^2=33 x^6+93 x^5+112 x^4+55 x^3+54 x^2+108 x+71$
• $y^2=3 x^6+50 x^5+38 x^4+5 x^3+93 x^2+15 x+48$
• $y^2=33 x^6+27 x^5+78 x^4+42 x^3+10 x^2+91 x+12$
• $y^2=104 x^6+66 x^5+5 x^4+30 x^3+27 x^2+25 x+39$
• $y^2=38 x^6+10 x^5+40 x^4+24 x^3+68 x^2+40 x+85$
• $y^2=5 x^6+58 x^5+96 x^4+63 x^3+49 x^2+97 x+94$
• $y^2=31 x^6+56 x^5+105 x^4+73 x^3+52 x^2+104 x+71$
• $y^2=58 x^6+104 x^5+31 x^4+65 x^3+100 x^2+29 x+32$
• $y^2=108 x^6+60 x^5+60 x^4+91 x^3+23 x^2+15 x+86$
• $y^2=55 x^6+91 x^5+93 x^4+83 x^3+39 x^2+26 x+32$
• $y^2=17 x^6+84 x^5+52 x^4+37 x^3+103 x^2+96 x+21$
• $y^2=34 x^6+60 x^5+82 x^4+61 x^3+10 x^2+81 x+91$
• $y^2=54 x^6+6 x^5+69 x^4+76 x^3+16 x^2+66 x+84$
• $y^2=34 x^6+56 x^5+56 x^4+78 x^3+75 x^2+39 x+78$
• $y^2=81 x^6+48 x^5+99 x^4+29 x^3+17 x^2+25 x+4$
• $y^2=45 x^6+60 x^5+102 x^4+77 x^3+108 x^2+6 x+23$
• $y^2=72 x^6+66 x^5+64 x^4+102 x^3+59 x^2+12 x+23$
• $y^2=19 x^6+3 x^5+61 x^4+86 x^3+78 x^2+21 x+20$
• $y^2=83 x^6+59 x^5+59 x^4+23 x^3+70 x^2+81 x+62$
• $y^2=108 x^6+103 x^5+108 x^4+37 x^3+14 x^2+101 x+66$
• $y^2=14 x^6+2 x^5+51 x^4+9 x^3+71 x^2+28 x+7$
• $y^2=24 x^6+20 x^5+103 x^4+92 x^3+100 x^2+46 x+85$
• $y^2=33 x^6+100 x^5+46 x^4+36 x^3+35 x^2+108 x+76$
• $y^2=101 x^6+67 x^5+28 x^4+32 x^3+59 x^2+53 x+81$
• $y^2=61 x^6+37 x^5+105 x^4+78 x^3+3 x^2+44 x+48$
• $y^2=75 x^6+82 x^5+64 x^4+51 x^3+76 x^2+50 x+35$
• $y^2=65 x^6+32 x^5+25 x^4+31 x^3+51 x^2+6 x+48$
• $y^2=93 x^6+105 x^5+82 x^4+99 x^3+22 x^2+11 x+43$
• $y^2=x^6+53 x^5+8 x^4+98 x^3+66 x^2+71 x+43$
• $y^2=98 x^6+38 x^5+21 x^4+32 x^3+100 x^2+80 x+81$
• $y^2=56 x^6+58 x^5+76 x^4+37 x^3+13 x^2+50 x+107$
• $y^2=25 x^6+101 x^5+92 x^4+72 x^3+43 x^2+21 x+78$
• $y^2=x^6+88 x^5+50 x^4+86 x^3+24 x^2+56 x+104$
• $y^2=58 x^6+102 x^5+8 x^3+88 x^2+86 x+37$
• $y^2=45 x^6+31 x^5+107 x^4+90 x^3+65 x^2+33 x+17$
• $y^2=59 x^6+77 x^5+x^4+52 x^3+40 x^2+104 x+89$
• $y^2=13 x^6+112 x^5+62 x^4+91 x^3+43 x^2+84 x+53$
• $y^2=36 x^6+6 x^5+109 x^4+105 x^3+72 x^2+16 x+28$
• $y^2=82 x^6+91 x^4+75 x^3+38 x^2+17 x+93$
• $y^2=107 x^6+34 x^5+91 x^4+97 x^3+10 x^2+8 x+80$
• $y^2=84 x^6+75 x^5+48 x^4+98 x^3+82 x^2+4 x+88$
• $y^2=110 x^6+2 x^5+48 x^4+56 x^3+88 x^2+60 x+104$
• $y^2=82 x^6+92 x^5+78 x^4+89 x^3+42 x^2+98 x+40$
• $y^2=21 x^6+48 x^5+49 x^4+77 x^3+7 x^2+78 x+63$
• $y^2=18 x^6+54 x^5+78 x^4+53 x^3+96 x^2+104 x+78$
• $y^2=37 x^6+94 x^5+92 x^4+88 x^3+88 x^2+30 x+21$
• $y^2=91 x^6+8 x^5+21 x^4+78 x^3+93 x^2+69 x+24$
• $y^2=93 x^6+7 x^5+97 x^4+17 x^3+2 x^2+43 x+96$
• $y^2=71 x^6+45 x^5+71 x^4+98 x^3+91 x^2+3 x+48$
• $y^2=90 x^6+31 x^5+12 x^4+76 x^3+105 x^2+38 x+40$
• $y^2=17 x^6+21 x^5+3 x^4+66 x^3+40 x^2+14 x+112$
• $y^2=49 x^6+61 x^5+22 x^4+2 x^3+102 x^2+11 x+17$
• $y^2=59 x^6+53 x^5+15 x^4+57 x^3+34 x^2+67 x+45$
• $y^2=29 x^6+82 x^5+65 x^3+77 x^2+12 x+47$
• $y^2=34 x^6+36 x^5+105 x^4+55 x^3+82 x^2+92 x+108$
• $y^2=50 x^6+12 x^5+51 x^4+81 x^3+101 x^2+16 x+101$
• $y^2=27 x^6+83 x^5+24 x^4+22 x^3+51 x^2+71$
• $y^2=24 x^6+22 x^5+99 x^4+15 x^3+82 x^2+92 x+70$
• $y^2=68 x^6+15 x^5+7 x^4+4 x^3+39 x^2+47 x+50$
• $y^2=11 x^6+10 x^5+94 x^4+6 x^3+104 x^2+107 x+4$
• $y^2=42 x^6+109 x^5+107 x^4+21 x^3+78 x^2+61 x+110$
• $y^2=94 x^6+25 x^5+73 x^4+86 x^3+64 x^2+9 x+56$

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 4.0.4290109200.1.

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_jf	$2$	(not in LMFDB)