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

• Label: 2.113.az_oj
• 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:	$1 - 25 x + 373 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.239051555039$, $\pm0.353240637974$
Angle rank:	$2$ (numerical)
Number field:	4.0.104456069.1
Galois group:	$D_{4}$
Jacobians:	$56$
Isomorphism classes:	56

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10293$	$164615949$	$2087549443341$	$26589691413337941$	$339457116683558773968$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12891$	$1446773$	$163079555$	$18424372294$	$2081949658947$	$235260529522093$	$26584441893772579$	$3004041937834588649$	$339456738976051429086$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=96 x^6+49 x^5+80 x^4+91 x^3+21 x^2+37 x+98$
• $y^2=109 x^6+72 x^5+11 x^4+39 x^3+88 x^2+69 x+95$
• $y^2=55 x^6+3 x^5+50 x^4+89 x^3+14 x^2+96 x+73$
• $y^2=66 x^6+85 x^5+98 x^4+42 x^3+55 x^2+99 x+35$
• $y^2=45 x^6+82 x^5+47 x^4+38 x^3+30 x^2+79 x+38$
• $y^2=55 x^6+111 x^5+86 x^4+20 x^3+60 x^2+37 x+23$
• $y^2=10 x^6+92 x^5+67 x^4+92 x^3+104 x+22$
• $y^2=72 x^6+96 x^5+19 x^4+76 x^3+43 x^2+31 x+103$
• $y^2=65 x^6+68 x^5+46 x^4+13 x^3+41 x^2+89 x+12$
• $y^2=35 x^6+75 x^5+6 x^4+111 x^3+90 x^2+60 x+50$
• $y^2=44 x^6+46 x^5+34 x^4+104 x^3+51 x^2+79 x+16$
• $y^2=16 x^6+45 x^5+5 x^4+18 x^3+92 x^2+111 x+73$
• $y^2=84 x^6+96 x^5+24 x^4+102 x^3+29 x^2+46 x+107$
• $y^2=16 x^6+72 x^5+108 x^4+44 x^3+109 x^2+58 x+24$
• $y^2=71 x^6+63 x^5+2 x^4+32 x^3+111 x^2+71 x+41$
• $y^2=86 x^6+108 x^5+54 x^4+31 x^3+64 x^2+93 x+30$
• $y^2=60 x^6+23 x^5+13 x^4+23 x^3+88 x^2+10 x+18$
• $y^2=37 x^6+3 x^5+106 x^4+45 x^3+30 x^2+54 x+66$
• $y^2=20 x^6+104 x^5+42 x^4+63 x^3+20 x^2+81 x+29$
• $y^2=111 x^6+107 x^5+71 x^4+21 x^3+81 x^2+108 x+55$
• and

• $y^2=6 x^6+39 x^5+98 x^4+54 x^3+5 x^2+48 x+55$
• $y^2=x^6+75 x^5+11 x^4+43 x^3+66 x^2+78 x+102$
• $y^2=62 x^6+27 x^5+93 x^4+54 x^3+72 x^2+22 x+62$
• $y^2=106 x^6+42 x^5+40 x^4+43 x^3+102 x^2+41 x+110$
• $y^2=44 x^6+10 x^5+66 x^4+21 x^3+12 x^2+34 x+23$
• $y^2=96 x^6+59 x^5+95 x^4+109 x^3+60 x^2+43 x+100$
• $y^2=100 x^6+96 x^5+27 x^4+84 x^3+23 x^2+x+73$
• $y^2=95 x^6+64 x^5+101 x^4+89 x^3+71 x^2+38 x+5$
• $y^2=81 x^6+51 x^5+90 x^4+44 x^3+92 x^2+110 x+91$
• $y^2=63 x^6+62 x^5+28 x^4+43 x^3+101 x^2+34 x+37$
• $y^2=46 x^6+35 x^5+55 x^4+31 x^3+58 x^2+86 x+75$
• $y^2=5 x^6+16 x^5+29 x^4+24 x^3+10 x^2+95 x+64$
• $y^2=40 x^6+2 x^5+24 x^4+64 x^3+43 x^2+48 x+12$
• $y^2=80 x^6+27 x^5+112 x^4+109 x^3+26 x^2+87 x+65$
• $y^2=19 x^6+86 x^5+70 x^4+102 x^3+83 x^2+8 x+18$
• $y^2=36 x^6+35 x^5+88 x^4+106 x^3+12 x^2+6 x+89$
• $y^2=79 x^6+90 x^5+26 x^4+101 x^3+85 x^2+80 x+12$
• $y^2=74 x^6+14 x^5+87 x^4+81 x^3+7 x^2+24 x+105$
• $y^2=24 x^6+49 x^5+39 x^4+57 x^3+71 x^2+106 x+46$
• $y^2=27 x^6+110 x^5+71 x^4+49 x^3+92 x^2+108 x+95$
• $y^2=47 x^6+5 x^5+105 x^4+79 x^3+9 x^2+45 x+2$
• $y^2=32 x^6+68 x^5+60 x^4+19 x^3+76 x^2+82 x+59$
• $y^2=35 x^6+97 x^5+93 x^4+22 x^3+35 x^2+68 x+34$
• $y^2=60 x^6+96 x^5+78 x^3+92 x^2+19 x+6$
• $y^2=78 x^6+5 x^5+74 x^4+82 x^3+x^2+28 x+61$
• $y^2=112 x^6+80 x^5+94 x^4+6 x^3+107 x^2+60 x+36$
• $y^2=107 x^6+87 x^5+69 x^4+38 x^3+63 x^2+21 x+47$
• $y^2=11 x^6+50 x^5+107 x^4+76 x^3+15 x^2+39 x+20$
• $y^2=58 x^6+3 x^5+92 x^4+29 x^3+68 x^2+7 x+14$
• $y^2=68 x^6+80 x^5+41 x^4+50 x^3+59 x+31$
• $y^2=18 x^6+17 x^5+43 x^4+105 x^3+69 x^2+17 x+82$
• $y^2=75 x^6+57 x^5+25 x^4+111 x^3+86 x^2+8 x+68$
• $y^2=46 x^6+18 x^5+76 x^4+17 x^3+94 x^2+50 x+35$
• $y^2=93 x^6+83 x^5+47 x^4+14 x^3+72 x^2+60 x+49$
• $y^2=87 x^6+4 x^5+89 x^4+104 x^3+48 x^2+3 x+6$
• $y^2=111 x^6+43 x^5+5 x^4+85 x^3+99 x^2+79 x+58$

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 4.0.104456069.1.

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_oj	$2$	(not in LMFDB)