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

• Label: 2.113.aw_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:	$1 - 22 x + 321 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.226550153570$, $\pm0.410474674324$
Angle rank:	$2$ (numerical)
Number field:	4.0.870049856.1
Galois group:	$D_{4}$
Jacobians:	$76$
Isomorphism classes:	152

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10583$	$165084217$	$2086401070844$	$26586631059958649$	$339456377808456483223$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12928$	$1445978$	$163060788$	$18424332192$	$2081952650998$	$235260568150112$	$26584441862831076$	$3004041932557027994$	$339456738932594145168$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 76 curves (of which all are hyperelliptic):

• $y^2=50 x^6+105 x^5+110 x^4+15 x^3+103 x^2+84 x+3$
• $y^2=32 x^6+24 x^5+64 x^4+95 x^3+58 x^2+87 x+19$
• $y^2=70 x^6+5 x^5+75 x^4+104 x^3+43 x^2+51 x+13$
• $y^2=74 x^6+111 x^5+63 x^4+51 x^3+20 x^2+36 x+62$
• $y^2=77 x^6+29 x^5+23 x^4+81 x^3+17 x^2+93 x+79$
• $y^2=16 x^6+47 x^5+93 x^4+9 x^3+30 x^2+40 x+81$
• $y^2=47 x^6+5 x^5+5 x^4+107 x^3+13 x^2+20 x+23$
• $y^2=40 x^6+68 x^5+45 x^4+26 x^3+38 x^2+11 x+43$
• $y^2=70 x^6+60 x^5+62 x^4+9 x^3+79 x^2+91 x+39$
• $y^2=x^6+59 x^5+68 x^4+30 x^3+80 x^2+96 x+76$
• $y^2=79 x^6+109 x^5+81 x^4+85 x^3+73 x^2+43 x+1$
• $y^2=45 x^6+35 x^5+17 x^4+6 x^3+55 x^2+2 x+19$
• $y^2=23 x^6+83 x^5+52 x^4+79 x^3+54 x^2+45 x+61$
• $y^2=53 x^6+106 x^5+37 x^4+24 x^3+49 x^2+103 x+67$
• $y^2=6 x^6+3 x^5+73 x^4+33 x^3+111 x^2+99 x+106$
• $y^2=79 x^6+5 x^5+61 x^4+93 x^3+68 x^2+112 x+69$
• $y^2=6 x^6+16 x^5+68 x^4+47 x^3+5 x^2+36 x+57$
• $y^2=37 x^6+94 x^5+111 x^4+93 x^3+83 x^2+56 x+49$
• $y^2=12 x^6+47 x^5+63 x^4+81 x^3+20 x^2+36 x+83$
• $y^2=50 x^6+4 x^5+14 x^4+65 x^3+94 x^2+35 x+22$
• and

• $y^2=109 x^6+64 x^5+44 x^4+12 x^3+35 x^2+8 x+64$
• $y^2=59 x^6+69 x^5+21 x^4+36 x^3+103 x^2+109 x+9$
• $y^2=23 x^6+54 x^5+82 x^4+68 x^3+20 x^2+6 x+108$
• $y^2=8 x^6+82 x^5+63 x^4+52 x^3+51 x^2+92 x+13$
• $y^2=31 x^6+42 x^5+62 x^4+51 x^3+2 x^2+45 x+64$
• $y^2=54 x^6+107 x^5+9 x^4+99 x^3+101 x^2+84 x+40$
• $y^2=109 x^6+27 x^5+73 x^4+38 x^3+95 x^2+14 x+57$
• $y^2=44 x^6+29 x^5+12 x^4+106 x^3+16 x^2+71 x+79$
• $y^2=29 x^6+54 x^5+10 x^4+84 x^3+27 x^2+7 x+43$
• $y^2=6 x^6+45 x^5+16 x^4+108 x^2+13 x+47$
• $y^2=78 x^6+45 x^5+84 x^4+78 x^3+97 x^2+107 x+77$
• $y^2=37 x^6+89 x^5+63 x^4+98 x^3+102 x^2+46 x+55$
• $y^2=96 x^6+41 x^5+72 x^4+10 x^3+67 x^2+43 x+82$
• $y^2=5 x^6+7 x^5+62 x^4+11 x^3+24 x^2+98 x+70$
• $y^2=23 x^6+20 x^5+87 x^4+57 x^3+108 x^2+54 x+25$
• $y^2=6 x^6+83 x^5+56 x^4+25 x^3+66 x^2+5 x+46$
• $y^2=39 x^6+51 x^5+92 x^4+86 x^3+61 x^2+59 x+102$
• $y^2=48 x^6+82 x^5+75 x^4+21 x^3+9 x^2+18 x+57$
• $y^2=14 x^6+38 x^5+19 x^4+40 x^3+51 x^2+82 x+37$
• $y^2=64 x^6+27 x^5+x^4+56 x^3+112 x^2+87 x+17$
• $y^2=6 x^6+61 x^5+80 x^4+111 x^3+84 x^2+9 x+27$
• $y^2=94 x^6+18 x^5+37 x^4+72 x^3+13 x^2+5 x+72$
• $y^2=77 x^6+80 x^5+89 x^4+106 x^3+36 x^2+96 x+19$
• $y^2=28 x^6+49 x^5+6 x^4+3 x^3+31 x^2+100 x+44$
• $y^2=95 x^6+74 x^5+87 x^4+51 x^3+84 x^2+21 x+104$
• $y^2=13 x^6+27 x^5+33 x^4+13 x^3+21 x^2+73 x+99$
• $y^2=73 x^6+72 x^5+98 x^4+105 x^3+108 x^2+45 x+73$
• $y^2=92 x^6+63 x^5+37 x^4+50 x^3+64 x^2+68 x+22$
• $y^2=53 x^6+23 x^5+43 x^4+22 x^3+31 x^2+76 x+78$
• $y^2=99 x^6+23 x^5+49 x^4+98 x^3+15 x^2+62 x+91$
• $y^2=104 x^6+57 x^5+30 x^4+42 x^3+24 x^2+55 x+105$
• $y^2=33 x^6+64 x^5+72 x^4+4 x^3+29 x^2+17 x+6$
• $y^2=19 x^6+66 x^5+33 x^4+34 x^3+101 x^2+65 x+54$
• $y^2=96 x^6+6 x^5+110 x^4+70 x^3+29 x^2+51 x+76$
• $y^2=55 x^6+83 x^5+42 x^4+7 x^3+49 x^2+42 x+29$
• $y^2=54 x^6+110 x^5+4 x^4+54 x^3+37 x^2+65 x+37$
• $y^2=34 x^6+98 x^5+66 x^4+2 x^3+80 x^2+108 x+2$
• $y^2=43 x^6+60 x^5+40 x^4+100 x^3+15 x^2+97 x+112$
• $y^2=13 x^6+21 x^5+101 x^4+88 x^3+72 x^2+2 x+20$
• $y^2=49 x^6+45 x^5+107 x^4+98 x^3+99 x^2+7 x+86$
• $y^2=75 x^6+49 x^5+90 x^4+30 x^3+82 x^2+103 x+86$
• $y^2=94 x^6+82 x^5+36 x^4+108 x^3+13 x^2+110 x+66$
• $y^2=92 x^6+28 x^5+3 x^4+17 x^3+39 x^2+46 x+51$
• $y^2=88 x^6+24 x^5+33 x^4+49 x^3+3 x^2+49 x+70$
• $y^2=45 x^6+81 x^5+92 x^4+102 x^3+62 x^2+5 x+68$
• $y^2=105 x^6+50 x^5+55 x^4+76 x^3+45 x^2+104 x+12$
• $y^2=70 x^6+29 x^5+2 x^4+8 x^3+73 x^2+31 x+48$
• $y^2=40 x^6+61 x^5+40 x^4+68 x^3+48 x^2+96 x+47$
• $y^2=6 x^6+78 x^5+57 x^4+88 x^3+44 x^2+11 x+16$
• $y^2=37 x^6+46 x^5+41 x^4+79 x^3+99 x^2+112 x+78$
• $y^2=107 x^6+82 x^5+19 x^4+95 x^3+45 x^2+41 x+66$
• $y^2=23 x^6+101 x^5+20 x^4+3 x^3+5 x^2+72 x+84$
• $y^2=31 x^6+110 x^5+50 x^4+5 x^3+25 x^2+68 x+5$
• $y^2=45 x^6+18 x^5+87 x^4+47 x^3+2 x^2+32 x+37$
• $y^2=55 x^6+72 x^5+109 x^4+71 x^3+13 x^2+49 x+33$
• $y^2=44 x^6+66 x^5+83 x^4+17 x^3+75 x^2+91 x+97$

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 4.0.870049856.1.

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_mj	$2$	(not in LMFDB)