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

• Label: 2.113.aw_jp
• 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:	$1 - 22 x + 249 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0587256576400$, $\pm0.483515829767$
Angle rank:	$2$ (numerical)
Number field:	4.0.438848.1
Galois group:	$D_{4}$
Jacobians:	$45$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10511$	$163204297$	$2079541353212$	$26577287230828889$	$339452438022934465951$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12784$	$1441226$	$163003476$	$18424118352$	$2081953209142$	$235260550464752$	$26584441599669924$	$3004041936736787402$	$339456739034214439584$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 45 curves (of which all are hyperelliptic):

• $y^2=66 x^6+49 x^5+40 x^4+19 x^3+15 x^2+77 x+72$
• $y^2=66 x^6+109 x^5+65 x^4+62 x^3+61 x^2+110 x+99$
• $y^2=103 x^6+59 x^5+51 x^4+40 x^3+73 x^2+83 x+41$
• $y^2=43 x^6+95 x^4+62 x^3+64 x^2+5 x+92$
• $y^2=7 x^6+37 x^5+109 x^4+9 x^3+53 x^2+65 x+95$
• $y^2=44 x^6+39 x^5+31 x^4+71 x^3+8 x^2+76 x+74$
• $y^2=23 x^6+48 x^5+34 x^4+102 x^3+39 x^2+92 x+43$
• $y^2=110 x^6+81 x^5+111 x^4+38 x^3+8 x^2+58 x+38$
• $y^2=107 x^6+85 x^5+91 x^4+6 x^3+36 x^2+92 x+94$
• $y^2=17 x^6+92 x^5+58 x^4+11 x^3+90 x^2+93 x+8$
• $y^2=23 x^6+51 x^5+3 x^4+67 x^3+x^2+49 x+96$
• $y^2=64 x^6+88 x^5+45 x^4+65 x^3+73 x^2+5 x+79$
• $y^2=81 x^6+5 x^5+56 x^4+102 x^3+71 x^2+81 x+46$
• $y^2=9 x^6+101 x^5+16 x^4+62 x^3+46 x^2+65 x+7$
• $y^2=43 x^6+32 x^5+24 x^4+78 x^3+95 x^2+81 x+39$
• $y^2=89 x^6+10 x^5+9 x^4+73 x^3+85 x^2+55 x+37$
• $y^2=51 x^6+109 x^5+104 x^4+18 x^3+67 x^2+65 x+110$
• $y^2=66 x^6+3 x^5+84 x^4+21 x^3+9 x^2+110 x+73$
• $y^2=56 x^6+75 x^5+9 x^4+20 x^3+30 x^2+50 x+94$
• $y^2=89 x^6+26 x^5+47 x^4+x^3+60 x^2+80 x+99$
• and

• $y^2=71 x^6+73 x^5+84 x^4+78 x^3+89 x^2+95 x+89$
• $y^2=16 x^6+95 x^5+108 x^4+45 x^3+47 x^2+103 x+55$
• $y^2=75 x^6+54 x^5+111 x^4+22 x^3+81 x^2+62 x+46$
• $y^2=19 x^6+6 x^5+104 x^4+93 x^3+10 x^2+109 x+40$
• $y^2=103 x^6+52 x^5+87 x^4+4 x^3+10 x^2+32 x+97$
• $y^2=49 x^6+2 x^5+19 x^4+10 x^3+32 x^2+56 x+67$
• $y^2=17 x^6+75 x^5+91 x^4+66 x^3+81 x^2+108 x+93$
• $y^2=35 x^6+13 x^5+40 x^4+65 x^3+8 x^2+38 x+6$
• $y^2=54 x^6+38 x^5+103 x^4+50 x^3+101 x^2+67 x+108$
• $y^2=5 x^6+54 x^5+100 x^4+10 x^3+31 x^2+83 x+104$
• $y^2=33 x^6+99 x^5+69 x^4+80 x^3+21 x^2+12 x+99$
• $y^2=105 x^6+25 x^5+72 x^4+82 x^3+34 x^2+83 x+33$
• $y^2=39 x^6+19 x^5+104 x^4+58 x^3+7 x^2+82 x+93$
• $y^2=40 x^6+72 x^5+62 x^4+56 x^3+70 x^2+47 x+19$
• $y^2=106 x^6+107 x^5+23 x^4+33 x^3+112 x^2+78 x+73$
• $y^2=55 x^6+91 x^5+59 x^4+57 x^3+59 x^2+110 x+39$
• $y^2=35 x^6+81 x^5+36 x^4+6 x^3+54 x^2+105 x+110$
• $y^2=23 x^6+54 x^5+32 x^4+62 x^3+20 x^2+102 x+17$
• $y^2=85 x^6+105 x^5+25 x^4+94 x^3+60 x^2+22 x+71$
• $y^2=65 x^6+33 x^5+7 x^4+x^3+70 x^2+12 x+46$
• $y^2=43 x^6+105 x^5+14 x^4+12 x^3+23 x^2+43 x+76$
• $y^2=106 x^6+93 x^5+25 x^4+4 x^3+24 x^2+26 x+27$
• $y^2=106 x^6+101 x^5+98 x^4+98 x^3+107 x^2+24 x+54$
• $y^2=59 x^6+53 x^5+45 x^4+31 x^3+58 x^2+94 x+51$
• $y^2=100 x^6+9 x^5+8 x^4+28 x^3+54 x^2+20 x+86$

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 4.0.438848.1.

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.w_jp	$2$	(not in LMFDB)