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

• Label: 2.113.ax_ms
• 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:	$1 - 23 x + 330 x^{2} - 2599 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.209605248996$, $\pm0.406040479496$
Angle rank:	$2$ (numerical)
Number field:	4.0.894187532.1
Galois group:	$D_{4}$
Jacobians:	$88$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10478$	$164735116$	$2086005169664$	$26586497576527616$	$339456704631971199598$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$12901$	$1445704$	$163059969$	$18424349931$	$2081953169506$	$235260578183995$	$26584441988868993$	$3004041933120148648$	$339456738920851398021$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 88 curves (of which all are hyperelliptic):

• $y^2=71 x^6+44 x^5+73 x^4+21 x^3+100 x^2+96 x+54$
• $y^2=66 x^6+27 x^5+10 x^4+89 x^3+109 x^2+111 x+29$
• $y^2=6 x^6+28 x^5+65 x^4+47 x^3+45 x^2+50 x+10$
• $y^2=108 x^6+41 x^5+68 x^4+44 x^3+14 x^2+55 x+67$
• $y^2=92 x^6+49 x^5+11 x^4+82 x^3+95 x^2+85 x+98$
• $y^2=20 x^6+67 x^5+109 x^4+76 x^3+94 x^2+44 x+12$
• $y^2=54 x^6+74 x^5+95 x^4+100 x^3+51 x^2+79 x+102$
• $y^2=31 x^6+17 x^5+38 x^4+106 x^3+9 x^2+19 x+27$
• $y^2=111 x^6+97 x^5+34 x^4+101 x^3+45 x^2+105 x+34$
• $y^2=91 x^6+71 x^5+55 x^4+93 x^3+70 x^2+85 x+92$
• $y^2=105 x^6+88 x^5+53 x^4+6 x^3+103 x^2+45 x+64$
• $y^2=90 x^6+59 x^5+109 x^4+32 x^3+23 x^2+102 x+30$
• $y^2=97 x^6+53 x^5+92 x^4+17 x^3+51 x^2+81 x+15$
• $y^2=85 x^6+54 x^5+9 x^4+90 x^3+98 x^2+26 x+34$
• $y^2=5 x^6+10 x^5+98 x^4+38 x^3+84 x^2+72 x+25$
• $y^2=38 x^6+77 x^5+x^4+96 x^3+64 x^2+72 x+43$
• $y^2=8 x^6+92 x^5+36 x^4+82 x^3+71 x^2+78 x+30$
• $y^2=84 x^6+77 x^5+106 x^4+94 x^3+44 x^2+22 x+89$
• $y^2=65 x^6+13 x^5+26 x^4+3 x^3+44 x^2+99 x+58$
• $y^2=79 x^6+63 x^5+100 x^4+64 x^3+57 x^2+89 x+5$
• and

• $y^2=73 x^6+98 x^5+15 x^4+94 x^3+78 x^2+70 x+77$
• $y^2=45 x^6+69 x^5+6 x^4+14 x^3+16 x^2+24 x+95$
• $y^2=90 x^6+21 x^5+19 x^4+12 x^3+87 x^2+16 x+4$
• $y^2=58 x^6+22 x^5+9 x^4+41 x^3+109 x^2+52 x+69$
• $y^2=86 x^6+10 x^5+21 x^4+54 x^3+50 x^2+34 x+71$
• $y^2=94 x^6+29 x^5+64 x^4+19 x^3+65 x^2+79 x+44$
• $y^2=2 x^6+44 x^5+53 x^4+x^3+107 x^2+107 x+46$
• $y^2=76 x^6+79 x^5+74 x^4+59 x^3+59 x^2+71 x+46$
• $y^2=100 x^6+18 x^5+57 x^4+80 x^3+6 x^2+32 x+42$
• $y^2=16 x^6+19 x^5+13 x^4+67 x^3+8 x^2+52 x+54$
• $y^2=62 x^6+49 x^5+83 x^4+28 x^3+37 x^2+69 x+80$
• $y^2=81 x^6+111 x^4+62 x^3+76 x^2+103 x+90$
• $y^2=29 x^6+9 x^5+48 x^4+65 x^3+51 x^2+47 x+45$
• $y^2=67 x^6+50 x^5+13 x^4+86 x^3+97 x^2+41 x+110$
• $y^2=83 x^6+85 x^5+106 x^4+55 x^3+49 x^2+80 x+34$
• $y^2=36 x^6+112 x^5+73 x^4+56 x^3+8 x^2+13 x+43$
• $y^2=51 x^6+57 x^5+10 x^4+107 x^3+54 x^2+31 x+102$
• $y^2=94 x^6+54 x^5+32 x^4+19 x^3+80 x^2+52 x+56$
• $y^2=24 x^6+81 x^5+5 x^4+37 x^3+51 x^2+81 x+45$
• $y^2=92 x^6+45 x^5+56 x^4+12 x^3+83 x^2+57 x+71$
• $y^2=89 x^6+62 x^5+81 x^4+78 x^3+36 x^2+99 x+56$
• $y^2=45 x^6+110 x^5+75 x^4+19 x^3+22 x^2+4 x+54$
• $y^2=6 x^6+72 x^5+49 x^4+4 x^3+31 x^2+99 x+16$
• $y^2=21 x^6+107 x^5+53 x^4+28 x^3+21 x+38$
• $y^2=38 x^6+90 x^5+36 x^4+53 x^3+36 x^2+21 x+33$
• $y^2=43 x^6+9 x^5+110 x^4+92 x^3+37 x^2+87 x+6$
• $y^2=24 x^6+48 x^5+20 x^4+50 x^3+11 x^2+9 x+6$
• $y^2=67 x^6+94 x^5+84 x^4+103 x^3+52 x^2+22 x+39$
• $y^2=11 x^6+97 x^5+6 x^4+32 x^3+29 x^2+86 x+45$
• $y^2=66 x^6+35 x^5+80 x^4+75 x^3+48 x^2+88 x+79$
• $y^2=104 x^6+27 x^5+72 x^4+48 x^3+61 x^2+63 x+90$
• $y^2=76 x^6+103 x^5+110 x^4+42 x^3+75 x^2+40 x+67$
• $y^2=86 x^6+88 x^5+49 x^4+106 x^3+65 x^2+46 x+24$
• $y^2=76 x^6+16 x^5+108 x^4+45 x^3+69 x^2+27 x+24$
• $y^2=57 x^6+54 x^5+11 x^4+18 x^3+33 x^2+13 x+5$
• $y^2=65 x^6+73 x^5+70 x^4+26 x^3+80 x^2+10 x+45$
• $y^2=98 x^6+51 x^5+50 x^4+72 x^3+110 x^2+111 x+15$
• $y^2=64 x^6+103 x^5+13 x^4+83 x^3+59 x^2+28 x+47$
• $y^2=6 x^6+42 x^5+54 x^4+41 x^3+98 x^2+62 x+79$
• $y^2=35 x^6+41 x^5+96 x^4+96 x^3+56 x^2+29 x+46$
• $y^2=36 x^6+42 x^5+96 x^4+67 x^3+73 x^2+39 x+97$
• $y^2=63 x^6+30 x^5+90 x^4+36 x^3+111 x^2+98 x+10$
• $y^2=7 x^6+30 x^5+79 x^4+106 x^3+103 x^2+108 x+71$
• $y^2=25 x^6+49 x^5+40 x^4+19 x^3+66 x^2+107 x+27$
• $y^2=34 x^6+92 x^5+48 x^4+104 x^3+4 x^2+99 x+17$
• $y^2=40 x^6+67 x^5+83 x^4+6 x^3+108 x^2+75 x+51$
• $y^2=81 x^6+102 x^5+63 x^4+63 x^3+30 x^2+80 x+110$
• $y^2=100 x^6+72 x^5+14 x^4+19 x^3+2 x^2+53 x+96$
• $y^2=27 x^6+40 x^5+5 x^4+14 x^3+108 x^2+71 x+74$
• $y^2=30 x^6+106 x^5+106 x^4+76 x^3+3 x^2+42 x+9$
• $y^2=53 x^6+15 x^5+44 x^4+112 x^3+17 x^2+94 x+20$
• $y^2=13 x^6+102 x^5+74 x^4+50 x^3+86 x^2+43 x+104$
• $y^2=43 x^6+74 x^5+85 x^4+73 x^3+103 x^2+x+40$
• $y^2=40 x^6+47 x^5+107 x^4+36 x^3+54 x^2+52 x+95$
• $y^2=39 x^6+92 x^5+102 x^4+66 x^3+26 x^2+111 x+96$
• $y^2=31 x^6+48 x^5+46 x^4+32 x^3+8 x^2+67 x+12$
• $y^2=34 x^6+34 x^5+30 x^4+81 x^3+51 x^2+8 x+82$
• $y^2=42 x^6+43 x^5+61 x^4+69 x^3+33 x^2+65 x+40$
• $y^2=9 x^6+103 x^5+44 x^4+110 x^3+39 x^2+81 x+60$
• $y^2=23 x^6+83 x^5+43 x^4+4 x^3+23 x^2+9 x+27$
• $y^2=13 x^6+13 x^5+110 x^4+71 x^3+38 x^2+95 x+107$
• $y^2=103 x^6+87 x^5+17 x^4+33 x^3+x^2+3 x+76$
• $y^2=30 x^6+62 x^5+75 x^4+23 x^3+87 x^2+41 x+76$
• $y^2=37 x^6+74 x^5+73 x^4+86 x^3+43 x^2+70 x+52$
• $y^2=11 x^6+51 x^5+11 x^4+30 x^3+22 x^2+22 x+104$
• $y^2=20 x^6+76 x^5+18 x^4+13 x^3+47 x^2+58 x+55$
• $y^2=108 x^6+5 x^5+3 x^4+105 x^3+22 x^2+61 x+102$
• $y^2=51 x^6+69 x^5+82 x^4+42 x^3+30 x^2+10 x+10$

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 4.0.894187532.1.

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_ms	$2$	(not in LMFDB)