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

• Label: 2.113.aw_mx
• 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:	$1 - 22 x + 335 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.261834682104$, $\pm0.384665101061$
Angle rank:	$2$ (numerical)
Number field:	4.0.13817232.1
Galois group:	$D_{4}$
Jacobians:	$72$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10597$	$165450961$	$2087735994448$	$26588055632650681$	$339454703797941461917$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12956$	$1446902$	$163069524$	$18424241332$	$2081949477086$	$235260538955716$	$26584441933809508$	$3004041936887048150$	$339456738972954493196$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=61 x^6+39 x^5+101 x^4+72 x^3+14 x^2+18 x+105$
• $y^2=74 x^6+35 x^5+5 x^4+59 x^3+84 x^2+59 x+2$
• $y^2=35 x^6+66 x^5+3 x^4+55 x^3+111 x^2+107 x+78$
• $y^2=71 x^6+100 x^5+103 x^4+9 x^3+32 x^2+2 x+17$
• $y^2=56 x^6+73 x^5+87 x^4+6 x^3+27 x^2+5 x+58$
• $y^2=10 x^6+2 x^5+87 x^4+53 x^3+105 x^2+105 x+52$
• $y^2=76 x^6+111 x^5+101 x^4+38 x^3+110 x^2+51 x+10$
• $y^2=x^6+67 x^5+81 x^4+102 x^3+2 x^2+53 x+58$
• $y^2=29 x^6+61 x^5+18 x^4+49 x^3+43 x^2+14 x+31$
• $y^2=4 x^6+22 x^5+97 x^4+93 x^3+71 x^2+87 x+18$
• $y^2=5 x^6+58 x^5+7 x^4+2 x^3+106 x^2+104 x+73$
• $y^2=94 x^6+6 x^5+77 x^4+36 x^3+72 x^2+18 x+5$
• $y^2=57 x^6+81 x^5+110 x^4+90 x^3+86 x^2+14 x+78$
• $y^2=87 x^6+66 x^5+29 x^4+53 x^3+108 x^2+71 x+63$
• $y^2=99 x^6+81 x^5+26 x^4+105 x^3+106 x^2+64 x+21$
• $y^2=89 x^6+59 x^5+45 x^4+x^3+82 x^2+65 x+80$
• $y^2=2 x^6+71 x^5+74 x^4+35 x^3+109 x^2+28 x+48$
• $y^2=43 x^6+8 x^5+79 x^4+76 x^3+107 x^2+35 x+29$
• $y^2=108 x^6+73 x^5+106 x^4+23 x^3+20 x^2+5 x+70$
• $y^2=4 x^6+77 x^5+41 x^4+54 x^3+103 x^2+33 x+23$
• and

• $y^2=23 x^6+21 x^5+71 x^4+110 x^3+85 x^2+63 x+85$
• $y^2=48 x^6+14 x^5+72 x^4+110 x^3+89 x^2+25 x+89$
• $y^2=81 x^6+23 x^5+48 x^4+23 x^3+55 x^2+75 x+79$
• $y^2=39 x^6+39 x^5+34 x^4+75 x^3+16 x^2+112 x+64$
• $y^2=12 x^6+65 x^5+4 x^4+90 x^3+3 x^2+102 x+39$
• $y^2=27 x^6+103 x^5+105 x^4+17 x^3+83 x^2+6 x+44$
• $y^2=86 x^6+51 x^5+55 x^4+90 x^3+56 x^2+87 x+28$
• $y^2=72 x^6+24 x^5+78 x^4+75 x^3+50 x^2+22 x+92$
• $y^2=91 x^6+68 x^5+24 x^4+80 x^3+74 x^2+70 x+111$
• $y^2=14 x^6+28 x^5+31 x^4+36 x^3+75 x^2+79 x+63$
• $y^2=101 x^6+24 x^5+75 x^4+3 x^3+51 x^2+100 x+111$
• $y^2=52 x^6+73 x^5+39 x^4+7 x^3+70 x^2+59 x+54$
• $y^2=37 x^6+82 x^5+57 x^4+105 x^3+82 x^2+15 x+93$
• $y^2=17 x^6+80 x^5+77 x^4+30 x^3+111 x^2+24 x+46$
• $y^2=59 x^6+49 x^5+21 x^4+8 x^3+57 x^2+87 x+60$
• $y^2=19 x^6+101 x^5+4 x^4+43 x^3+x^2+3 x+15$
• $y^2=23 x^6+102 x^5+64 x^4+43 x^3+2 x^2+36 x+68$
• $y^2=100 x^6+91 x^5+87 x^4+24 x^3+31 x^2+84 x+68$
• $y^2=x^6+29 x^5+88 x^4+98 x^3+4 x^2+80 x+81$
• $y^2=26 x^6+52 x^5+108 x^4+34 x^3+88 x^2+42 x+105$
• $y^2=58 x^6+42 x^5+35 x^4+105 x^3+26 x^2+66 x+54$
• $y^2=45 x^6+78 x^5+54 x^4+91 x^3+90 x^2+62 x+86$
• $y^2=55 x^6+22 x^5+6 x^4+101 x^3+47 x^2+78 x+91$
• $y^2=67 x^6+53 x^5+45 x^4+46 x^3+96 x^2+23 x+84$
• $y^2=48 x^6+86 x^5+58 x^4+92 x^3+102 x^2+25 x+109$
• $y^2=86 x^6+28 x^5+101 x^4+31 x^3+9 x^2+47 x+76$
• $y^2=73 x^6+25 x^5+50 x^4+11 x^3+66 x^2+25 x+3$
• $y^2=88 x^6+3 x^5+8 x^4+96 x^3+32 x^2+78 x+84$
• $y^2=89 x^6+111 x^5+35 x^4+67 x^3+19 x^2+26 x+109$
• $y^2=30 x^6+x^5+100 x^4+112 x^3+20 x^2+10 x+40$
• $y^2=107 x^6+47 x^5+75 x^4+35 x^3+79 x^2+52 x+98$
• $y^2=26 x^6+98 x^5+101 x^4+12 x^3+92 x^2+4 x+74$
• $y^2=59 x^6+43 x^5+7 x^4+89 x^2+37 x+74$
• $y^2=71 x^6+112 x^5+57 x^4+20 x^3+71 x^2+25 x+51$
• $y^2=90 x^6+34 x^5+3 x^4+41 x^3+42 x^2+106 x+72$
• $y^2=76 x^6+106 x^5+46 x^4+67 x^3+22 x^2+42 x+105$
• $y^2=18 x^6+80 x^5+85 x^4+86 x^3+42 x^2+32 x+43$
• $y^2=87 x^6+4 x^5+18 x^4+21 x^3+41 x^2+33 x+101$
• $y^2=96 x^6+70 x^5+69 x^4+19 x^3+22 x^2+102 x+21$
• $y^2=60 x^6+44 x^5+80 x^4+16 x^3+60 x^2+92 x+84$
• $y^2=82 x^6+2 x^5+45 x^4+19 x^3+45 x^2+38 x+68$
• $y^2=107 x^6+111 x^5+100 x^4+45 x^3+111 x^2+79 x+24$
• $y^2=107 x^6+77 x^5+81 x^4+102 x^3+75 x^2+84 x+22$
• $y^2=42 x^6+64 x^5+20 x^4+25 x^3+94 x^2+67 x+55$
• $y^2=53 x^6+106 x^5+56 x^4+79 x^3+28 x^2+31 x+78$
• $y^2=x^6+51 x^5+84 x^4+76 x^3+48 x^2+53 x+41$
• $y^2=72 x^6+98 x^5+68 x^4+42 x^3+83 x^2+82 x+75$
• $y^2=18 x^6+93 x^5+33 x^4+103 x^3+105 x+58$
• $y^2=35 x^6+49 x^5+48 x^4+37 x^3+56 x^2+3 x+30$
• $y^2=48 x^6+11 x^5+76 x^4+27 x^3+57 x^2+79 x+106$
• $y^2=76 x^6+104 x^5+85 x^4+70 x^3+87 x^2+28 x+107$
• $y^2=70 x^6+71 x^5+105 x^4+107 x^3+112 x^2+15 x+46$

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 4.0.13817232.1.

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_mx	$2$	(not in LMFDB)