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

• Label: 2.113.az_ma
• 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:	$1 - 25 x + 312 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0601744223071$, $\pm0.437945754370$
Angle rank:	$2$ (numerical)
Number field:	4.0.137076296.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10232$	$163016224$	$2080941922304$	$26578452721579136$	$339449671022827141432$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12769$	$1442198$	$163010625$	$18423968169$	$2081951659198$	$235260570556793$	$26584441906362369$	$3004041935027601974$	$339456738990177773889$

Jacobians and polarizations

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

• $y^2=83 x^6+99 x^5+73 x^4+93 x^3+68 x^2+39 x+4$
• $y^2=34 x^6+17 x^5+31 x^4+22 x^3+5 x+31$
• $y^2=101 x^6+25 x^5+67 x^4+108 x^3+49 x^2+10 x+51$
• $y^2=22 x^6+68 x^5+88 x^4+64 x^3+29 x^2+54 x+18$
• $y^2=67 x^6+15 x^5+30 x^4+112 x^3+85 x^2+27 x+75$
• $y^2=108 x^6+87 x^5+44 x^4+48 x^3+19 x^2+90 x+42$
• $y^2=42 x^6+72 x^5+87 x^4+4 x^3+74 x^2+36 x+63$
• $y^2=33 x^6+40 x^5+45 x^4+112 x^3+43 x+75$
• $y^2=84 x^6+103 x^5+13 x^4+38 x^3+50 x^2+22 x+76$
• $y^2=12 x^6+17 x^5+4 x^4+31 x^3+33 x^2+95 x+57$
• $y^2=41 x^6+3 x^5+23 x^4+42 x^3+86 x^2+3 x+13$
• $y^2=33 x^6+6 x^5+68 x^4+8 x^3+26 x^2+107 x$
• $y^2=110 x^6+x^5+76 x^4+83 x^3+37 x^2+6 x+73$
• $y^2=45 x^6+47 x^5+44 x^4+90 x^3+102 x^2+5$
• $y^2=79 x^6+38 x^5+107 x^4+48 x^3+20 x^2+63 x+13$
• $y^2=107 x^6+84 x^5+65 x^4+18 x^3+17 x^2+88 x+28$
• $y^2=29 x^6+21 x^5+72 x^4+42 x^3+27 x^2+93 x+76$
• $y^2=74 x^6+85 x^5+103 x^4+37 x^3+100 x^2+27 x+108$
• $y^2=14 x^6+80 x^5+95 x^4+94 x^3+52 x^2+4 x+20$
• $y^2=48 x^6+44 x^5+3 x^4+2 x^3+18 x^2+81 x+10$
• and

• $y^2=24 x^6+64 x^5+7 x^4+24 x^3+15 x^2+75 x+8$
• $y^2=101 x^6+59 x^5+42 x^4+102 x^3+22 x^2+71 x+97$
• $y^2=64 x^6+11 x^5+5 x^4+21 x^3+102 x^2+92 x+81$
• $y^2=46 x^6+85 x^5+28 x^4+58 x^3+39 x^2+87 x+112$
• $y^2=16 x^6+79 x^5+12 x^4+60 x^3+44 x^2+60 x+67$
• $y^2=40 x^6+39 x^5+5 x^4+83 x^3+96 x^2+60 x+3$
• $y^2=65 x^6+44 x^5+25 x^4+30 x^3+25 x^2+64 x+28$
• $y^2=96 x^6+106 x^5+25 x^4+61 x^3+96 x^2+87 x+67$
• $y^2=8 x^6+12 x^5+41 x^4+67 x^3+44 x^2+6 x+58$
• $y^2=64 x^6+43 x^5+93 x^4+79 x^3+74 x^2+96 x+86$
• $y^2=24 x^6+96 x^5+24 x^4+99 x^3+12 x^2+102 x+18$
• $y^2=51 x^6+56 x^5+54 x^4+95 x^3+23 x^2+103$
• $y^2=5 x^6+33 x^5+42 x^4+17 x^3+15 x^2+19 x+45$
• $y^2=2 x^6+38 x^5+66 x^4+29 x^3+49 x^2+77 x+61$
• $y^2=53 x^6+74 x^5+76 x^4+36 x^3+83 x^2+6 x+95$
• $y^2=93 x^6+12 x^5+71 x^4+49 x^3+100 x^2+55 x+84$
• $y^2=13 x^6+16 x^5+27 x^4+34 x^3+50 x^2+86 x+86$
• $y^2=8 x^6+63 x^5+19 x^4+69 x^3+25 x^2+72 x+53$
• $y^2=78 x^6+90 x^5+71 x^4+2 x^3+8 x^2+61 x+108$
• $y^2=76 x^6+73 x^5+44 x^4+70 x^3+17 x^2+99 x+67$
• $y^2=78 x^6+14 x^5+66 x^4+89 x^3+111 x^2+55 x+29$
• $y^2=86 x^6+59 x^5+8 x^4+64 x^3+40 x^2+33 x+59$
• $y^2=48 x^6+42 x^5+52 x^4+53 x^3+19 x^2+71 x+101$
• $y^2=51 x^6+44 x^5+42 x^4+80 x^3+42 x^2+110 x+80$
• $y^2=53 x^6+53 x^5+66 x^4+64 x^3+67 x^2+18 x+104$
• $y^2=53 x^6+3 x^5+12 x^4+29 x^3+112 x^2+13 x+26$
• $y^2=50 x^6+26 x^5+41 x^4+47 x^3+81 x^2+95 x+72$
• $y^2=69 x^6+10 x^5+56 x^4+99 x^3+112 x^2+102 x+108$
• $y^2=54 x^6+13 x^5+99 x^4+9 x^3+90 x^2+31 x+91$
• $y^2=50 x^6+95 x^5+111 x^4+63 x^3+40 x^2+36 x+47$
• $y^2=71 x^6+2 x^5+30 x^4+42 x^3+5 x^2+47 x+92$
• $y^2=56 x^6+51 x^5+100 x^4+100 x^3+43 x^2+23 x+40$
• $y^2=80 x^6+11 x^5+42 x^4+50 x^3+93 x^2+79 x+77$
• $y^2=88 x^6+65 x^5+78 x^4+21 x^3+64 x^2+103 x+5$
• $y^2=74 x^6+46 x^5+5 x^4+4 x^3+83 x^2+76 x+102$
• $y^2=78 x^6+56 x^5+53 x^4+36 x^3+35 x^2+85 x+112$
• $y^2=48 x^6+49 x^5+110 x^4+108 x^3+7 x^2+32 x+70$
• $y^2=112 x^6+12 x^5+91 x^4+27 x^3+28 x^2+4 x+55$
• $y^2=42 x^6+19 x^5+52 x^4+29 x^3+67 x^2+54$
• $y^2=34 x^6+20 x^5+32 x^4+41 x^3+110 x^2+56 x+19$
• $y^2=55 x^6+43 x^5+76 x^4+8 x^3+88 x^2+94 x$
• $y^2=94 x^6+30 x^5+62 x^4+36 x^3+68 x^2+100 x+13$
• $y^2=87 x^6+29 x^5+94 x^4+47 x^3+32 x^2+33 x+73$
• $y^2=98 x^6+109 x^5+41 x^4+64 x^3+91 x^2+94 x+31$
• $y^2=83 x^6+56 x^5+70 x^4+32 x^3+4 x^2+8 x+13$
• $y^2=47 x^6+84 x^5+27 x^4+86 x^3+7 x^2+33 x+52$
• $y^2=71 x^6+81 x^5+43 x^4+77 x^3+57 x^2+11 x+27$
• $y^2=87 x^6+107 x^5+79 x^4+37 x^3+3 x^2+71 x+38$
• $y^2=76 x^6+57 x^5+47 x^4+42 x^3+84 x^2+66 x+24$
• $y^2=84 x^6+44 x^5+37 x^3+31 x^2+23 x+24$
• $y^2=47 x^6+103 x^5+69 x^4+8 x^3+53 x^2+5 x+109$
• $y^2=26 x^6+33 x^5+72 x^4+73 x^3+94 x^2+17 x+30$

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 4.0.137076296.1.

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.z_ma	$2$	(not in LMFDB)