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

• Label: 2.113.ax_my
• 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:	$1 - 23 x + 336 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.223832413730$, $\pm0.396637575746$
Angle rank:	$2$ (numerical)
Number field:	4.0.37989116.2
Galois group:	$D_{4}$
Jacobians:	$84$
Isomorphism classes:	84

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10484$	$164892352$	$2086603219664$	$26587264602270464$	$339456399528740273524$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12913$	$1446118$	$163064673$	$18424333371$	$2081952055198$	$235260565069579$	$26584441950038721$	$3004041933768029254$	$339456738928585026993$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 84 curves (of which all are hyperelliptic):

• $y^2=50 x^6+7 x^5+12 x^4+89 x^3+99 x^2+43$
• $y^2=90 x^6+25 x^5+14 x^4+19 x^3+99 x^2+66 x+18$
• $y^2=86 x^6+11 x^5+55 x^4+38 x^3+73 x^2+105 x+80$
• $y^2=9 x^6+22 x^5+94 x^4+7 x^3+37 x^2+96 x+52$
• $y^2=98 x^6+69 x^5+102 x^4+12 x^3+55 x^2+62 x+9$
• $y^2=73 x^6+13 x^5+95 x^4+34 x^3+23 x^2+84 x+85$
• $y^2=102 x^6+64 x^5+103 x^4+88 x^3+2 x^2+40 x+79$
• $y^2=108 x^6+71 x^5+14 x^4+x^3+26 x^2+97 x+105$
• $y^2=94 x^6+61 x^5+110 x^4+64 x^3+39 x^2+21 x+70$
• $y^2=38 x^6+86 x^5+91 x^4+48 x^3+78 x^2+48 x+84$
• $y^2=85 x^6+73 x^5+71 x^4+57 x^3+88 x^2+52 x+66$
• $y^2=93 x^6+36 x^5+102 x^4+49 x^3+71 x^2+14 x+12$
• $y^2=30 x^6+11 x^5+79 x^4+55 x^3+72 x^2+53 x+34$
• $y^2=25 x^6+44 x^5+15 x^4+38 x^3+6 x^2+100 x+54$
• $y^2=79 x^6+75 x^5+69 x^4+95 x^3+27 x^2+30 x+42$
• $y^2=74 x^6+73 x^5+65 x^4+23 x^3+71 x^2+21 x+59$
• $y^2=77 x^6+107 x^5+107 x^4+2 x^3+39 x^2+37 x+55$
• $y^2=39 x^6+82 x^5+93 x^4+12 x^3+7 x^2+109 x+34$
• $y^2=89 x^6+8 x^5+91 x^4+111 x^3+89 x^2+35 x+84$
• $y^2=68 x^6+2 x^5+51 x^4+111 x^3+81 x^2+54 x+8$
• and

• $y^2=108 x^5+57 x^4+82 x^3+92 x^2+82 x+21$
• $y^2=83 x^6+61 x^5+61 x^4+79 x^3+106 x^2+49 x+81$
• $y^2=56 x^6+88 x^5+79 x^4+40 x^3+16 x^2+20 x+17$
• $y^2=103 x^6+44 x^5+78 x^4+14 x^3+98 x^2+12 x+76$
• $y^2=46 x^6+72 x^5+108 x^4+x^3+17 x^2+4 x+13$
• $y^2=111 x^6+77 x^5+41 x^4+102 x^3+32 x^2+102 x+16$
• $y^2=92 x^6+78 x^5+27 x^4+76 x^3+55 x^2+38 x+86$
• $y^2=22 x^6+18 x^5+x^4+9 x^3+92 x^2+107 x+87$
• $y^2=44 x^6+46 x^5+107 x^4+68 x^3+63 x^2+78 x+85$
• $y^2=89 x^6+35 x^5+49 x^4+22 x^3+101 x^2+109$
• $y^2=17 x^6+73 x^5+107 x^4+32 x^3+79 x^2+11 x+68$
• $y^2=49 x^6+72 x^5+7 x^4+28 x^3+47 x^2+3 x+79$
• $y^2=79 x^6+82 x^5+69 x^4+41 x^3+83 x^2+31 x+6$
• $y^2=63 x^6+82 x^5+12 x^4+29 x^3+44 x^2+72 x+61$
• $y^2=45 x^6+43 x^5+56 x^4+29 x^3+111 x^2+31 x+89$
• $y^2=103 x^6+37 x^5+88 x^4+75 x^3+55 x^2+73 x+67$
• $y^2=83 x^6+91 x^5+86 x^3+40 x^2+101 x+63$
• $y^2=8 x^6+82 x^5+95 x^4+78 x^3+48 x^2+91 x+80$
• $y^2=39 x^6+66 x^5+38 x^4+88 x^3+48 x^2+11 x+86$
• $y^2=33 x^6+104 x^5+46 x^4+22 x^3+105 x^2+83 x+96$
• $y^2=6 x^6+31 x^5+71 x^4+5 x^3+44 x^2+51 x+45$
• $y^2=17 x^6+24 x^5+55 x^4+50 x^3+13 x^2+97 x+46$
• $y^2=x^6+22 x^5+12 x^4+80 x^3+112 x^2+39 x+27$
• $y^2=50 x^6+67 x^5+109 x^4+33 x^3+45 x^2+10 x+90$
• $y^2=45 x^6+106 x^5+57 x^4+33 x^3+30 x^2+24 x+80$
• $y^2=58 x^6+86 x^4+73 x^3+107 x^2+42 x+64$
• $y^2=46 x^6+62 x^5+107 x^4+60 x^3+82 x^2+38 x+9$
• $y^2=108 x^6+88 x^5+9 x^4+102 x^3+72 x^2+100 x+75$
• $y^2=30 x^6+10 x^5+60 x^4+85 x^3+15 x^2+103 x+90$
• $y^2=69 x^6+59 x^5+32 x^4+92 x^3+111 x^2+26 x+70$
• $y^2=22 x^6+42 x^5+104 x^4+100 x^3+4 x^2+45 x+67$
• $y^2=101 x^6+53 x^5+19 x^4+68 x^3+33 x^2+92 x$
• $y^2=15 x^6+6 x^5+109 x^4+100 x^3+38 x^2+58 x+8$
• $y^2=73 x^6+34 x^5+91 x^4+76 x^3+19 x^2+26 x+45$
• $y^2=110 x^6+47 x^5+45 x^4+106 x^3+112 x^2+49 x$
• $y^2=19 x^6+53 x^5+4 x^4+58 x^3+54 x^2+103 x+88$
• $y^2=23 x^6+111 x^5+23 x^4+89 x^3+87 x^2+40 x+60$
• $y^2=111 x^6+49 x^5+103 x^4+103 x^3+87 x^2+88 x+98$
• $y^2=27 x^6+60 x^5+52 x^4+2 x^3+39 x^2+102 x+92$
• $y^2=58 x^6+11 x^5+42 x^4+112 x^3+82 x^2+19 x+30$
• $y^2=106 x^6+108 x^5+6 x^4+110 x^3+18 x^2+80 x+84$
• $y^2=85 x^6+8 x^5+73 x^4+41 x^3+13 x^2+102 x+1$
• $y^2=78 x^6+53 x^5+47 x^4+20 x^3+30 x^2+62 x+78$
• $y^2=55 x^6+105 x^5+44 x^4+100 x^3+98 x^2+112 x+40$
• $y^2=76 x^6+44 x^5+53 x^4+104 x^3+65 x^2+58 x+78$
• $y^2=36 x^6+41 x^5+62 x^4+53 x^3+4 x^2+90 x+108$
• $y^2=61 x^6+111 x^5+57 x^4+108 x^3+18 x^2+22 x+36$
• $y^2=42 x^6+101 x^5+20 x^4+56 x^3+54 x^2+28 x+78$
• $y^2=43 x^6+78 x^5+58 x^4+71 x^3+78 x^2+102 x+90$
• $y^2=39 x^6+67 x^5+8 x^4+91 x^3+30 x^2+16 x+108$
• $y^2=10 x^6+13 x^5+75 x^4+74 x^3+76 x^2+110 x+97$
• $y^2=106 x^6+67 x^5+75 x^4+99 x^3+102 x^2+68 x+69$
• $y^2=27 x^6+57 x^5+91 x^4+91 x^3+79 x^2+42 x+22$
• $y^2=109 x^6+88 x^5+14 x^4+104 x^3+52 x^2+11 x+15$
• $y^2=93 x^6+48 x^5+60 x^4+111 x^3+69 x^2+22 x+108$
• $y^2=98 x^6+13 x^5+24 x^3+45 x^2+94 x+65$
• $y^2=70 x^6+79 x^5+67 x^4+13 x^3+101 x^2+32 x+87$
• $y^2=51 x^6+29 x^5+105 x^4+88 x^3+64 x^2+57 x+12$
• $y^2=65 x^6+34 x^5+21 x^4+52 x^3+72 x^2+46 x+51$
• $y^2=44 x^6+91 x^5+37 x^4+2 x^2+83 x+45$
• $y^2=39 x^6+30 x^5+87 x^4+110 x^3+57 x^2+60 x+26$
• $y^2=46 x^6+87 x^5+27 x^4+93 x^3+12 x^2+95 x+89$
• $y^2=101 x^6+109 x^5+102 x^4+14 x^3+43 x^2+71 x+40$
• $y^2=75 x^6+51 x^5+66 x^4+93 x^3+57 x^2+49 x+47$

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 4.0.37989116.2.

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_my	$2$	(not in LMFDB)