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

• Label: 2.113.az_mj
• 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:	$1 - 25 x + 321 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0947042427355$, $\pm0.429448010261$
Angle rank:	$2$ (numerical)
Number field:	4.0.417725.1
Galois group:	$D_{4}$
Jacobians:	$64$
Isomorphism classes:	72

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10241$	$163251781$	$2081916331649$	$26580263341397381$	$339451847369149681936$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12787$	$1442873$	$163021731$	$18424086294$	$2081953054963$	$235260593740793$	$26584442230653123$	$3004041937924897049$	$339456739006389413022$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 64 curves (of which all are hyperelliptic):

• $y^2=105 x^6+23 x^5+14 x^4+27 x^3+74 x^2+35 x+29$
• $y^2=15 x^6+100 x^5+56 x^4+20 x^3+74 x^2+95 x+25$
• $y^2=48 x^6+81 x^5+47 x^4+59 x^3+94 x^2+52 x+112$
• $y^2=51 x^6+64 x^5+23 x^4+10 x^3+98 x^2+52 x+107$
• $y^2=70 x^6+68 x^5+72 x^4+75 x^3+73 x^2+42 x+61$
• $y^2=105 x^6+84 x^5+95 x^4+102 x^3+2 x^2+84 x+51$
• $y^2=37 x^6+26 x^5+11 x^4+61 x^3+25 x^2+26 x+52$
• $y^2=43 x^6+79 x^5+24 x^4+61 x^3+112 x^2+12 x+40$
• $y^2=27 x^6+46 x^5+40 x^4+12 x^3+27 x^2+41 x+58$
• $y^2=70 x^6+13 x^5+66 x^4+108 x^3+7 x^2+62 x+34$
• $y^2=20 x^6+x^5+104 x^4+42 x^3+60 x^2+101 x+31$
• $y^2=33 x^6+x^5+3 x^4+99 x^3+60 x^2+56 x+58$
• $y^2=52 x^6+39 x^5+96 x^4+82 x^3+90 x^2+39 x+52$
• $y^2=64 x^6+74 x^5+30 x^4+105 x^3+74 x^2+94 x+89$
• $y^2=94 x^6+106 x^5+16 x^4+83 x^3+73 x^2+27 x+6$
• $y^2=94 x^6+54 x^5+8 x^4+109 x^3+68 x^2+68 x+6$
• $y^2=67 x^6+27 x^5+92 x^4+44 x^3+2 x^2+97 x+57$
• $y^2=90 x^6+97 x^5+87 x^4+61 x^3+72 x^2+110 x+12$
• $y^2=7 x^6+59 x^5+78 x^4+63 x^2+88 x+84$
• $y^2=37 x^6+64 x^5+17 x^4+6 x^3+85 x^2+56 x+53$
• and

• $y^2=104 x^6+98 x^5+91 x^4+86 x^3+x^2+104 x+47$
• $y^2=20 x^6+63 x^5+14 x^4+11 x^3+37 x^2+11 x+17$
• $y^2=93 x^6+15 x^5+35 x^4+38 x^3+57 x^2+45 x+35$
• $y^2=5 x^5+60 x^4+74 x^3+62 x^2+52 x+103$
• $y^2=99 x^6+14 x^5+44 x^4+50 x^3+68 x^2+45 x+72$
• $y^2=26 x^6+15 x^5+99 x^4+45 x^3+37 x^2+93 x+18$
• $y^2=35 x^6+31 x^5+102 x^4+83 x^3+46 x^2+2 x+54$
• $y^2=8 x^6+30 x^5+52 x^4+70 x^3+14 x^2+21 x+102$
• $y^2=x^6+80 x^5+77 x^4+112 x^3+55 x^2+88 x+108$
• $y^2=14 x^6+81 x^5+101 x^4+59 x^3+53 x^2+17 x+25$
• $y^2=41 x^6+24 x^5+72 x^4+63 x^3+54 x^2+76 x+45$
• $y^2=16 x^6+84 x^5+83 x^4+98 x^3+4 x^2+77 x+18$
• $y^2=33 x^6+74 x^5+42 x^4+15 x^3+23 x^2+24 x+17$
• $y^2=103 x^6+24 x^5+51 x^4+75 x^3+8 x^2+83 x+73$
• $y^2=77 x^6+34 x^5+29 x^4+36 x^3+19 x^2+91 x+23$
• $y^2=82 x^6+74 x^5+112 x^4+30 x^3+70 x^2+54 x+66$
• $y^2=58 x^6+67 x^5+101 x^4+25 x^3+93 x^2+5 x+111$
• $y^2=47 x^6+51 x^5+62 x^4+27 x^3+71 x^2+48 x+73$
• $y^2=43 x^6+75 x^5+46 x^4+98 x^3+82 x^2+77 x+84$
• $y^2=41 x^6+28 x^5+2 x^4+45 x^3+15 x^2+96 x+104$
• $y^2=58 x^6+48 x^5+18 x^4+86 x^3+10 x^2+52 x+99$
• $y^2=6 x^6+37 x^5+16 x^4+12 x^3+44 x^2+43 x+79$
• $y^2=109 x^6+3 x^5+65 x^4+81 x^3+93 x^2+73 x+30$
• $y^2=5 x^6+52 x^5+10 x^4+94 x^3+67 x^2+52 x+19$
• $y^2=97 x^6+67 x^5+13 x^4+5 x^3+17 x^2+98 x+33$
• $y^2=60 x^6+92 x^5+34 x^4+42 x^3+94 x^2+25 x+24$
• $y^2=96 x^6+103 x^5+30 x^4+101 x^3+65 x^2+70 x+108$
• $y^2=51 x^6+82 x^5+70 x^4+110 x^3+60 x^2+39 x+73$
• $y^2=27 x^6+61 x^5+63 x^4+39 x^3+97 x^2+22 x+102$
• $y^2=102 x^6+90 x^5+27 x^4+90 x^3+60 x^2+50 x+82$
• $y^2=8 x^6+61 x^5+92 x^4+84 x^3+45 x^2+76 x+29$
• $y^2=11 x^6+34 x^5+65 x^4+66 x^3+8 x^2+43 x+7$
• $y^2=17 x^6+104 x^5+17 x^4+99 x^3+35 x^2+102 x+45$
• $y^2=90 x^6+92 x^5+14 x^4+94 x^3+49 x^2+87 x+26$
• $y^2=78 x^6+6 x^5+8 x^4+21 x^3+49 x^2+21 x+14$
• $y^2=100 x^6+34 x^5+4 x^4+78 x^3+97 x^2+112 x+100$
• $y^2=35 x^6+108 x^5+73 x^4+74 x^3+66 x^2+5 x+44$
• $y^2=110 x^6+37 x^5+31 x^4+27 x^3+x^2+93 x+47$
• $y^2=48 x^6+85 x^5+70 x^4+8 x^3+3 x^2+53 x+46$
• $y^2=2 x^6+111 x^5+109 x^4+94 x^3+x^2+43 x+100$
• $y^2=23 x^6+104 x^5+74 x^4+52 x^3+x^2+87 x+66$
• $y^2=35 x^6+108 x^5+25 x^4+90 x^3+55 x^2+10 x+55$
• $y^2=60 x^6+81 x^5+21 x^4+57 x^3+87 x^2+17 x+40$
• $y^2=79 x^6+83 x^5+75 x^4+109 x^3+99 x^2+72 x+23$

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 4.0.417725.1.

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_mj	$2$	(not in LMFDB)