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

• Label: 2.113.aw_jt
• 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:	$1 - 22 x + 253 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0735436140508$, $\pm0.480454596499$
Angle rank:	$2$ (numerical)
Number field:	4.0.1508906048.1
Galois group:	$D_{4}$
Jacobians:	$62$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10515$	$163308465$	$2079922224780$	$26577894980342025$	$339453208158436368075$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12792$	$1441490$	$163007204$	$18424160152$	$2081953915254$	$235260562254376$	$26584441730881156$	$3004041937852630130$	$339456739047176776632$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 62 curves (of which all are hyperelliptic):

• $y^2=29 x^6+28 x^5+111 x^4+71 x^3+75 x^2+45 x+40$
• $y^2=98 x^6+21 x^5+25 x^4+112 x^3+10 x^2+33 x+108$
• $y^2=43 x^6+11 x^5+71 x^4+18 x^3+87 x^2+100 x+101$
• $y^2=102 x^6+15 x^5+13 x^4+81 x^3+38 x^2+65 x+48$
• $y^2=24 x^6+36 x^5+4 x^4+99 x^3+68 x^2+59 x+64$
• $y^2=71 x^6+54 x^5+3 x^4+92 x^2+40 x+70$
• $y^2=6 x^6+49 x^5+60 x^4+98 x^3+24 x^2+65$
• $y^2=107 x^6+47 x^5+10 x^4+35 x^3+104 x^2+102 x+56$
• $y^2=82 x^6+105 x^5+90 x^4+38 x^3+81 x^2+15 x+39$
• $y^2=60 x^6+72 x^5+6 x^4+91 x^3+34 x^2+3 x+35$
• $y^2=54 x^6+26 x^5+112 x^4+77 x^3+64 x^2+48 x+88$
• $y^2=21 x^6+112 x^5+79 x^4+4 x^3+30 x^2+52 x+99$
• $y^2=107 x^6+101 x^5+51 x^4+96 x^3+15 x^2+106 x+3$
• $y^2=95 x^6+62 x^5+52 x^4+47 x^3+80 x^2+67 x+2$
• $y^2=99 x^6+74 x^5+39 x^4+84 x^3+73 x^2+34 x+28$
• $y^2=77 x^6+18 x^5+96 x^4+101 x^3+31 x^2+95 x+19$
• $y^2=66 x^6+90 x^5+82 x^3+7 x^2+41 x+46$
• $y^2=27 x^6+103 x^4+72 x^3+89 x^2+19 x+96$
• $y^2=22 x^6+29 x^5+88 x^4+10 x^3+44 x^2+65 x+84$
• $y^2=16 x^6+42 x^5+42 x^4+20 x^3+24 x^2+49 x+15$
• and

• $y^2=45 x^6+51 x^5+110 x^4+95 x^3+86 x^2+27 x+63$
• $y^2=70 x^6+75 x^5+91 x^4+52 x^3+71 x^2+40 x+14$
• $y^2=8 x^6+44 x^5+111 x^4+83 x^3+40 x^2+36 x+46$
• $y^2=38 x^6+25 x^5+107 x^4+87 x^3+46 x^2+14 x+45$
• $y^2=27 x^6+32 x^5+109 x^4+93 x^3+96 x^2+40 x+32$
• $y^2=91 x^6+33 x^5+75 x^4+87 x^3+96 x^2+12 x+41$
• $y^2=90 x^6+101 x^5+91 x^4+98 x^3+54 x^2+40 x+11$
• $y^2=112 x^6+75 x^5+14 x^4+86 x^3+55 x^2+38 x+78$
• $y^2=95 x^6+78 x^5+60 x^4+58 x^3+39 x^2+2 x+3$
• $y^2=98 x^6+17 x^5+18 x^4+48 x^3+11 x^2+94 x+82$
• $y^2=66 x^6+52 x^5+49 x^4+66 x^3+82 x^2+44 x+63$
• $y^2=26 x^6+89 x^5+6 x^4+86 x^3+5 x^2+2 x+101$
• $y^2=3 x^6+43 x^5+64 x^4+75 x^3+75 x^2+43 x+100$
• $y^2=48 x^6+83 x^5+3 x^4+52 x^3+112 x^2+81 x+94$
• $y^2=59 x^6+109 x^5+38 x^4+34 x^3+102 x^2+27 x+6$
• $y^2=82 x^6+25 x^5+94 x^4+81 x^3+7 x^2+54 x+110$
• $y^2=93 x^6+45 x^5+76 x^4+34 x^3+11 x^2+6 x+3$
• $y^2=103 x^6+x^5+95 x^4+58 x^3+33 x^2+22 x+42$
• $y^2=49 x^6+35 x^5+106 x^4+15 x^3+74 x^2+102 x+81$
• $y^2=71 x^6+100 x^5+81 x^4+24 x^3+6 x^2+58 x+36$
• $y^2=11 x^6+89 x^5+61 x^4+2 x^3+22 x^2+2 x+79$
• $y^2=80 x^6+108 x^5+103 x^4+74 x^3+59 x^2+71 x+108$
• $y^2=8 x^6+48 x^5+36 x^4+80 x^3+20 x^2+50 x+107$
• $y^2=80 x^6+33 x^5+40 x^4+82 x^3+58 x^2+43 x+74$
• $y^2=53 x^6+89 x^5+84 x^4+111 x^3+48 x^2+27 x+28$
• $y^2=106 x^6+51 x^5+64 x^4+21 x^3+58 x^2+109 x+109$
• $y^2=110 x^6+95 x^5+80 x^4+81 x^3+15 x^2+99 x+56$
• $y^2=34 x^6+61 x^5+76 x^4+49 x^3+75 x^2+48 x+17$
• $y^2=74 x^6+25 x^5+29 x^4+73 x^3+46 x^2+90 x+65$
• $y^2=7 x^6+45 x^5+69 x^4+101 x^3+23 x^2+91 x+43$
• $y^2=42 x^6+95 x^5+14 x^4+92 x^3+43 x^2+30 x+90$
• $y^2=85 x^6+4 x^5+39 x^4+72 x^3+68 x^2+68 x+16$
• $y^2=72 x^6+100 x^5+86 x^4+34 x^3+14 x^2+109 x+43$
• $y^2=79 x^6+74 x^5+74 x^3+57 x^2+19 x+54$
• $y^2=39 x^6+79 x^5+91 x^4+65 x^3+110 x^2+38 x+13$
• $y^2=22 x^6+80 x^5+105 x^4+51 x^3+43 x^2+59 x+105$
• $y^2=35 x^6+73 x^5+9 x^4+65 x^3+92 x^2+53 x+84$
• $y^2=101 x^6+30 x^5+16 x^4+85 x^3+37 x^2+34 x+90$
• $y^2=63 x^6+112 x^5+24 x^4+48 x^3+17 x^2+75 x+112$
• $y^2=x^6+10 x^5+81 x^4+43 x^3+38 x^2+6 x+100$
• $y^2=104 x^6+24 x^5+35 x^4+50 x^3+24 x^2+53 x+104$
• $y^2=92 x^6+5 x^4+93 x^3+9 x^2+94 x+3$

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 4.0.1508906048.1.

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_jt	$2$	(not in LMFDB)