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

• Label: 2.113.ax_mc
• 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:	$1 - 23 x + 314 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.174291261718$, $\pm0.426772364711$
Angle rank:	$2$ (numerical)
Number field:	4.0.1644521868.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10462$	$164316172$	$2084410714624$	$26584337512478464$	$339456772444253709022$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12869$	$1444600$	$163046721$	$18424353611$	$2081955155042$	$235260602331419$	$26584442122199809$	$3004041934200111256$	$339456738942187382309$

Jacobians and polarizations

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

• $y^2=77 x^6+21 x^5+109 x^4+87 x^3+96 x^2+14 x+21$
• $y^2=106 x^6+91 x^5+33 x^4+20 x^3+26 x^2+63 x+1$
• $y^2=86 x^6+42 x^5+100 x^4+78 x^3+49 x^2+111 x+10$
• $y^2=68 x^6+96 x^5+42 x^4+27 x^3+112 x^2+4 x$
• $y^2=42 x^6+32 x^5+30 x^4+7 x^3+88 x^2+104 x+44$
• $y^2=49 x^6+58 x^5+82 x^4+11 x^3+76 x^2+2 x+49$
• $y^2=68 x^6+51 x^5+56 x^4+3 x^3+76 x^2+90 x+64$
• $y^2=29 x^6+49 x^5+37 x^4+5 x^3+54 x^2+104 x+6$
• $y^2=100 x^6+10 x^5+104 x^4+24 x^3+32 x^2+3 x+39$
• $y^2=19 x^6+59 x^5+21 x^4+90 x^3+x^2+75 x+88$
• $y^2=23 x^6+71 x^5+9 x^4+78 x^3+49 x^2+61 x+102$
• $y^2=64 x^6+106 x^5+101 x^4+96 x^3+60 x^2+70 x+110$
• $y^2=48 x^6+73 x^5+18 x^4+87 x^3+103 x^2+23 x+94$
• $y^2=49 x^6+27 x^5+40 x^4+50 x^3+89 x^2+50 x+49$
• $y^2=83 x^6+48 x^5+33 x^4+22 x^3+69 x^2+86 x+12$
• $y^2=55 x^6+21 x^5+99 x^4+94 x^3+35 x^2+92 x+47$
• $y^2=103 x^6+101 x^5+86 x^4+45 x^3+86 x^2+21 x+40$
• $y^2=71 x^6+67 x^5+11 x^4+67 x^3+45 x^2+x+44$
• $y^2=71 x^6+73 x^5+59 x^4+59 x^3+26 x^2+73 x+86$
• $y^2=27 x^6+48 x^5+26 x^4+52 x^3+55 x^2+22 x+38$
• and

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

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 4.0.1644521868.1.

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.x_mc	$2$	(not in LMFDB)