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

• Label: 2.113.aw_nc
• 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:	$1 - 22 x + 340 x^{2} - 2486 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.278170435414$, $\pm0.371454266103$
Angle rank:	$2$ (numerical)
Number field:	4.0.79644992.1
Galois group:	$D_{4}$
Jacobians:	$88$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10602$	$165582036$	$2088212847498$	$26588533466815056$	$339453913411302301242$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$12966$	$1447232$	$163072454$	$18424198432$	$2081948118966$	$235260527285596$	$26584442006142718$	$3004041939663168860$	$339456738997742047446$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 88 curves (of which all are hyperelliptic):

• $y^2=108 x^6+57 x^5+46 x^4+49 x^3+25 x^2+28$
• $y^2=73 x^6+57 x^5+x^4+11 x^3+67 x^2+79 x+108$
• $y^2=109 x^6+53 x^5+15 x^4+100 x^3+94 x^2+23 x+77$
• $y^2=47 x^6+50 x^5+99 x^4+62 x^3+78 x^2+44 x+37$
• $y^2=86 x^6+37 x^5+88 x^4+38 x^3+83 x^2+67 x+85$
• $y^2=67 x^6+x^5+21 x^4+92 x^3+10 x^2+105 x+57$
• $y^2=95 x^6+39 x^5+11 x^4+22 x^3+52 x^2+14 x+68$
• $y^2=51 x^6+56 x^5+97 x^4+49 x^3+57 x^2+101 x+48$
• $y^2=43 x^6+27 x^5+101 x^4+19 x^3+65 x^2+65 x+50$
• $y^2=95 x^6+48 x^5+71 x^4+7 x^3+85 x^2+99 x+64$
• $y^2=69 x^6+86 x^5+109 x^4+42 x^3+25 x^2+76 x+11$
• $y^2=13 x^5+48 x^4+82 x^3+71 x^2+71 x+13$
• $y^2=33 x^6+21 x^5+112 x^4+16 x^3+86 x^2+78 x+71$
• $y^2=54 x^6+41 x^5+58 x^4+100 x^3+71 x^2+59 x+92$
• $y^2=43 x^6+41 x^5+62 x^4+60 x^3+85 x^2+16 x+7$
• $y^2=87 x^6+41 x^5+108 x^4+31 x^3+59 x^2+45 x+97$
• $y^2=110 x^6+90 x^5+71 x^4+107 x^3+75 x^2+95 x+43$
• $y^2=15 x^6+111 x^5+12 x^4+94 x^3+93 x^2+67 x+44$
• $y^2=31 x^6+55 x^5+105 x^4+13 x^3+6 x^2+70 x+100$
• $y^2=16 x^6+108 x^5+79 x^4+7 x^3+17 x^2+22 x+103$
• and

• $y^2=7 x^6+48 x^5+53 x^4+51 x^3+74 x^2+81 x+10$
• $y^2=30 x^6+47 x^5+57 x^4+93 x^3+15 x^2+29 x+20$
• $y^2=55 x^6+61 x^4+69 x^3+7 x^2+34 x+15$
• $y^2=30 x^6+95 x^5+70 x^4+65 x^3+105 x^2+80 x+100$
• $y^2=93 x^6+6 x^5+84 x^4+60 x^3+101 x^2+50 x+5$
• $y^2=10 x^6+8 x^5+36 x^4+22 x^3+38 x^2+25$
• $y^2=62 x^6+68 x^5+50 x^4+34 x^3+27 x^2+56 x+67$
• $y^2=105 x^6+54 x^5+30 x^4+25 x^3+18 x^2+45 x+67$
• $y^2=11 x^6+80 x^5+x^4+33 x^3+32 x^2+60 x+70$
• $y^2=34 x^6+110 x^5+44 x^4+59 x^3+77 x^2+83 x+39$
• $y^2=63 x^6+87 x^5+86 x^4+43 x^3+17 x^2+45 x+19$
• $y^2=110 x^6+7 x^5+12 x^4+69 x^3+29 x^2+65 x+13$
• $y^2=105 x^6+109 x^5+39 x^4+99 x^3+101 x^2+29 x+43$
• $y^2=47 x^6+27 x^5+87 x^4+56 x^3+62 x^2+79 x+74$
• $y^2=76 x^6+86 x^5+18 x^4+89 x^3+22 x^2+104 x+81$
• $y^2=67 x^6+109 x^5+19 x^4+67 x^3+58 x^2+43 x+101$
• $y^2=56 x^6+44 x^5+112 x^4+39 x^3+25 x^2+3 x+99$
• $y^2=83 x^6+93 x^5+55 x^4+10 x^3+19 x^2+16 x+58$
• $y^2=100 x^6+70 x^5+41 x^4+8 x^3+100 x^2+25 x+91$
• $y^2=69 x^6+22 x^5+45 x^4+98 x^3+109 x^2+18 x+54$
• $y^2=68 x^6+37 x^5+105 x^4+79 x^3+70 x^2+27 x+24$
• $y^2=90 x^6+22 x^5+38 x^4+57 x^3+75 x^2+85 x+43$
• $y^2=33 x^6+10 x^5+98 x^4+58 x^3+19 x^2+99 x+89$
• $y^2=107 x^6+17 x^5+104 x^4+88 x^3+13 x^2+111 x+46$
• $y^2=32 x^6+111 x^5+95 x^4+28 x^3+65 x^2+6 x+40$
• $y^2=19 x^6+65 x^5+93 x^4+18 x^3+62 x^2+62 x+71$
• $y^2=54 x^6+73 x^5+55 x^4+24 x^3+3 x^2+35 x+24$
• $y^2=50 x^6+105 x^5+78 x^4+94 x^3+61 x^2+110 x+46$
• $y^2=71 x^6+27 x^5+11 x^4+90 x^3+108 x^2+43 x+68$
• $y^2=106 x^6+69 x^5+22 x^4+52 x^3+16 x^2+14 x+63$
• $y^2=59 x^6+108 x^5+x^4+71 x^3+21 x^2+79 x+5$
• $y^2=108 x^6+20 x^5+64 x^4+89 x^3+80 x^2+51 x+88$
• $y^2=44 x^6+87 x^5+66 x^4+54 x^3+64 x^2+69 x+108$
• $y^2=111 x^6+99 x^5+67 x^4+26 x^3+38 x^2+105 x+86$
• $y^2=83 x^6+81 x^5+73 x^4+13 x^3+87 x+41$
• $y^2=82 x^6+35 x^5+63 x^4+10 x^3+30 x^2+69 x+60$
• $y^2=46 x^6+40 x^5+60 x^4+4 x^3+5 x^2+93 x+72$
• $y^2=39 x^6+106 x^5+40 x^4+107 x^3+39 x^2+7 x+102$
• $y^2=71 x^6+18 x^5+100 x^4+20 x^3+29 x^2+84 x+35$
• $y^2=98 x^6+12 x^5+60 x^4+57 x^3+45 x^2+106 x+64$
• $y^2=51 x^6+108 x^5+101 x^4+40 x^3+49 x^2+29 x+75$
• $y^2=12 x^6+105 x^5+79 x^4+53 x^3+9 x^2+83 x+8$
• $y^2=47 x^6+23 x^5+57 x^4+84 x^3+19 x^2+104 x+2$
• $y^2=55 x^6+72 x^5+81 x^4+50 x^3+66 x^2+95 x+112$
• $y^2=51 x^6+89 x^5+45 x^4+96 x^3+63 x^2+51 x+3$
• $y^2=79 x^6+6 x^5+45 x^4+72 x^3+17 x^2+96 x+92$
• $y^2=59 x^6+62 x^5+86 x^4+2 x^3+54 x^2+37 x+76$
• $y^2=111 x^6+105 x^5+88 x^4+6 x^3+64 x^2+57 x+44$
• $y^2=69 x^6+56 x^5+65 x^4+73 x^3+56 x^2+80 x+78$
• $y^2=85 x^6+64 x^5+74 x^4+55 x^3+44 x^2+56 x+24$
• $y^2=3 x^6+65 x^5+96 x^4+97 x^3+10 x^2+43 x+65$
• $y^2=17 x^6+71 x^5+77 x^3+21 x^2+72 x+54$
• $y^2=105 x^5+63 x^4+55 x^3+21 x^2+73 x+67$
• $y^2=110 x^6+97 x^5+6 x^4+10 x^3+71 x^2+100 x+71$
• $y^2=83 x^6+9 x^5+6 x^4+60 x^3+72 x^2+74 x+108$
• $y^2=92 x^6+28 x^5+61 x^4+13 x^3+73 x^2+50 x+52$
• $y^2=39 x^6+104 x^5+73 x^4+50 x^3+15 x^2+89 x+92$
• $y^2=43 x^6+10 x^5+112 x^4+27 x^3+108 x^2+51 x+91$
• $y^2=70 x^6+23 x^5+105 x^4+60 x^3+38 x^2+59 x+67$
• $y^2=8 x^6+65 x^5+49 x^4+56 x^3+102 x^2+103 x+15$
• $y^2=17 x^6+20 x^5+34 x^4+16 x^3+27 x^2+91 x+102$
• $y^2=54 x^6+43 x^5+95 x^4+34 x^3+90 x^2+98 x+44$
• $y^2=59 x^6+28 x^5+7 x^4+65 x^3+104 x^2+48 x+55$
• $y^2=112 x^6+73 x^5+79 x^4+x^3+21 x^2+42 x+41$
• $y^2=82 x^6+42 x^5+48 x^4+109 x^3+42 x^2+21 x+54$
• $y^2=27 x^6+28 x^5+71 x^4+94 x^3+66 x^2+65 x+101$
• $y^2=99 x^6+36 x^5+46 x^4+108 x^3+29 x^2+19 x+80$
• $y^2=76 x^6+2 x^5+81 x^4+24 x^3+90 x^2+52 x+92$

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 4.0.79644992.1.

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_nc	$2$	(not in LMFDB)