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

• Label: 2.113.au_jn
• 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:	$1 - 20 x + 247 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.151799378182$, $\pm0.483346408495$
Angle rank:	$2$ (numerical)
Number field:	4.0.4286718224.1
Galois group:	$D_{4}$
Jacobians:	$72$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10737$	$164243889$	$2082012228324$	$26581744914888681$	$339459080750331318657$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12864$	$1442938$	$163030820$	$18424478894$	$2081957270598$	$235260589115198$	$26584441885999684$	$3004041937826304634$	$339456739022059877664$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=32 x^6+4 x^5+55 x^4+70 x^3+88 x^2+67 x+5$
• $y^2=70 x^6+8 x^5+11 x^4+93 x^3+31 x^2+32 x+111$
• $y^2=14 x^6+105 x^5+104 x^4+14 x^3+82 x^2+81 x+110$
• $y^2=49 x^6+70 x^5+82 x^4+110 x^3+42 x^2+27 x+92$
• $y^2=44 x^6+18 x^5+46 x^4+81 x^3+72 x^2+42 x+112$
• $y^2=59 x^6+18 x^5+94 x^4+19 x^3+89 x^2+19 x+18$
• $y^2=12 x^6+72 x^5+107 x^4+16 x^3+109 x^2+26 x+109$
• $y^2=103 x^6+23 x^5+37 x^4+80 x^3+9 x^2+34 x+98$
• $y^2=40 x^6+44 x^5+71 x^4+17 x^3+95 x^2+13 x+78$
• $y^2=65 x^6+72 x^5+45 x^4+90 x^3+28 x^2+24 x+42$
• $y^2=55 x^6+12 x^5+37 x^4+37 x^3+10 x^2+12 x+105$
• $y^2=68 x^6+26 x^5+37 x^4+13 x^3+22 x^2+66 x+61$
• $y^2=45 x^6+105 x^5+51 x^4+82 x^3+109 x^2+19 x+86$
• $y^2=20 x^6+55 x^5+99 x^4+99 x^3+41 x^2+35 x+5$
• $y^2=73 x^6+33 x^5+5 x^4+90 x^3+82 x^2+29 x+102$
• $y^2=111 x^6+66 x^5+95 x^4+12 x^3+51 x^2+96 x+53$
• $y^2=65 x^6+52 x^5+74 x^4+91 x^3+83 x^2+100 x+107$
• $y^2=73 x^6+102 x^5+67 x^4+67 x^3+46 x^2+8 x+12$
• $y^2=33 x^6+10 x^5+88 x^4+20 x^3+64 x^2+22 x+44$
• $y^2=5 x^6+43 x^5+73 x^4+80 x^3+84 x^2+97 x+7$
• and

• $y^2=54 x^6+27 x^5+43 x^4+94 x^3+41 x^2+44 x+13$
• $y^2=47 x^6+112 x^5+108 x^4+92 x^3+63 x^2+62 x+4$
• $y^2=107 x^6+18 x^5+10 x^4+83 x^3+59 x^2+49 x+97$
• $y^2=35 x^6+25 x^5+91 x^4+19 x^3+59 x^2+83 x+13$
• $y^2=86 x^6+37 x^5+88 x^4+105 x^3+79 x^2+30 x+8$
• $y^2=54 x^6+5 x^5+30 x^4+110 x^3+104 x^2+35 x+13$
• $y^2=18 x^6+44 x^5+51 x^4+81 x^3+112 x^2+44 x+66$
• $y^2=6 x^6+108 x^5+31 x^4+28 x^3+27 x^2+69 x+89$
• $y^2=89 x^6+97 x^5+39 x^4+10 x^3+25 x^2+89 x+9$
• $y^2=73 x^6+102 x^5+48 x^4+34 x^3+67 x^2+54 x+3$
• $y^2=7 x^6+65 x^5+74 x^4+97 x^3+22 x^2+103 x+60$
• $y^2=55 x^6+82 x^5+26 x^4+22 x^3+44 x^2+x+57$
• $y^2=58 x^6+41 x^5+81 x^4+28 x^3+97 x^2+74 x+106$
• $y^2=11 x^6+20 x^5+58 x^4+65 x^3+8 x^2+5 x+70$
• $y^2=67 x^6+36 x^5+71 x^4+5 x^3+31 x^2+58 x+19$
• $y^2=15 x^6+77 x^5+84 x^4+82 x^3+47 x^2+77 x+77$
• $y^2=85 x^6+35 x^5+8 x^4+32 x^3+55 x^2+111 x+53$
• $y^2=71 x^6+67 x^5+83 x^4+95 x^3+77 x^2+57 x+29$
• $y^2=55 x^6+8 x^5+7 x^4+70 x^3+109 x^2+77 x+17$
• $y^2=8 x^6+43 x^5+57 x^4+60 x^3+77 x^2+75 x+16$
• $y^2=108 x^6+85 x^5+96 x^4+89 x^3+80 x^2+97 x+2$
• $y^2=7 x^6+37 x^5+64 x^3+103 x^2+49 x+110$
• $y^2=107 x^6+99 x^5+60 x^4+112 x^3+65 x^2+88 x+2$
• $y^2=24 x^6+18 x^4+11 x^3+71 x^2+23 x+76$
• $y^2=96 x^6+48 x^5+53 x^4+52 x^3+52 x^2+11 x+58$
• $y^2=105 x^6+108 x^5+3 x^4+5 x^3+106 x^2+89 x+83$
• $y^2=58 x^6+64 x^5+98 x^4+84 x^3+109 x^2+76 x+25$
• $y^2=55 x^6+107 x^5+91 x^4+105 x^3+70 x^2+108 x+96$
• $y^2=34 x^6+21 x^5+92 x^4+79 x^3+32 x^2+30 x+79$
• $y^2=98 x^6+21 x^5+62 x^4+106 x^3+4 x^2+10 x+70$
• $y^2=110 x^6+10 x^5+75 x^4+74 x^3+71 x^2+88 x+9$
• $y^2=30 x^6+63 x^5+110 x^4+50 x^3+98 x^2+23 x+47$
• $y^2=48 x^6+47 x^5+36 x^4+67 x^3+88 x^2+88 x+55$
• $y^2=55 x^6+76 x^5+23 x^3+30 x^2+49$
• $y^2=95 x^6+6 x^5+89 x^4+96 x^3+91 x^2+3 x+38$
• $y^2=74 x^6+33 x^5+91 x^4+92 x^3+18 x^2+29 x+46$
• $y^2=102 x^6+112 x^5+47 x^4+97 x^3+63 x^2+22 x+91$
• $y^2=24 x^6+60 x^5+72 x^4+84 x^3+90 x^2+61$
• $y^2=17 x^6+65 x^5+24 x^4+2 x^3+48 x^2+47 x+61$
• $y^2=58 x^6+88 x^5+4 x^4+12 x^3+74 x^2+30 x+85$
• $y^2=55 x^6+111 x^5+37 x^4+105 x^3+69 x^2+6 x+106$
• $y^2=12 x^6+33 x^5+41 x^4+92 x^3+82 x^2+77 x+90$
• $y^2=85 x^6+54 x^5+30 x^4+8 x^3+107 x^2+88 x+40$
• $y^2=4 x^6+59 x^5+74 x^4+42 x^3+101 x+47$
• $y^2=90 x^6+22 x^5+25 x^4+93 x^3+106 x^2+110 x+107$
• $y^2=56 x^6+59 x^5+36 x^4+44 x^3+26 x^2+49 x+75$
• $y^2=21 x^6+21 x^5+25 x^4+53 x^3+58 x^2+108 x+37$
• $y^2=58 x^6+43 x^5+97 x^4+25 x^3+18 x^2+73 x+17$
• $y^2=25 x^6+35 x^5+73 x^4+54 x^3+43 x^2+22 x+90$
• $y^2=59 x^6+102 x^5+62 x^3+58 x^2+100 x+75$
• $y^2=65 x^6+67 x^5+4 x^4+16 x^3+67 x^2+55 x+97$
• $y^2=49 x^6+2 x^5+102 x^4+32 x^3+42 x^2+28 x+9$

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 4.0.4286718224.1.

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_jn	$2$	(not in LMFDB)