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

• Label: 2.113.au_ih
• 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:	$1 - 20 x + 215 x^{2} - 2260 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0833455384368$, $\pm0.508020676869$
Angle rank:	$2$ (numerical)
Number field:	4.0.2697017616.1
Galois group:	$D_{4}$
Jacobians:	$68$
Isomorphism classes:	136

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10705$	$163411825$	$2079242298340$	$26578218409515625$	$339456073907576181025$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$12800$	$1441018$	$163009188$	$18424315694$	$2081954606150$	$235260550609598$	$26584441772706628$	$3004041941215647994$	$339456739059826364000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 68 curves (of which all are hyperelliptic):

• $y^2=x^6+60 x^5+30 x^4+67 x^3+9 x^2+23 x+42$
• $y^2=28 x^6+31 x^5+63 x^4+84 x^3+105 x^2+98 x+72$
• $y^2=83 x^6+57 x^5+60 x^4+93 x^3+92 x^2+66 x+80$
• $y^2=66 x^6+43 x^5+100 x^4+106 x^3+13 x^2+30 x+48$
• $y^2=39 x^6+7 x^5+3 x^4+14 x^3+46 x^2+35 x+9$
• $y^2=42 x^6+61 x^5+89 x^4+4 x^3+86 x^2+8 x+100$
• $y^2=47 x^6+83 x^5+80 x^4+74 x^3+55 x^2+71 x+75$
• $y^2=90 x^6+112 x^5+38 x^4+97 x^3+19 x^2+41 x+52$
• $y^2=3 x^6+77 x^5+106 x^4+28 x^3+4 x^2+34 x+15$
• $y^2=6 x^6+80 x^5+71 x^4+88 x^3+62 x^2+66$
• $y^2=65 x^6+x^5+10 x^4+4 x^3+4 x^2+104 x+54$
• $y^2=64 x^6+78 x^5+86 x^4+101 x^3+69 x^2+97 x+34$
• $y^2=71 x^6+84 x^5+34 x^4+32 x^3+70 x^2+106 x+90$
• $y^2=20 x^6+60 x^5+10 x^4+97 x^3+28 x^2+19 x+110$
• $y^2=65 x^6+103 x^5+111 x^4+20 x^3+85 x^2+110 x+64$
• $y^2=77 x^6+53 x^5+22 x^4+16 x^3+104 x^2+7 x+59$
• $y^2=23 x^6+20 x^5+7 x^4+42 x^3+26 x^2+19 x+64$
• $y^2=112 x^6+51 x^4+112 x^3+45 x^2+90 x+5$
• $y^2=84 x^6+22 x^5+111 x^4+31 x^3+106 x^2+29 x+72$
• $y^2=79 x^6+22 x^5+3 x^4+95 x^3+62 x^2+34 x+72$
• and

• $y^2=24 x^6+25 x^5+70 x^4+20 x^3+111 x^2+109 x+69$
• $y^2=8 x^6+14 x^5+52 x^4+10 x^3+80 x^2+70 x+110$
• $y^2=107 x^6+87 x^5+23 x^4+62 x^3+62 x^2+48 x+102$
• $y^2=16 x^6+111 x^5+50 x^4+61 x^3+44 x^2+71 x+90$
• $y^2=x^6+27 x^5+98 x^4+15 x^3+61 x^2+65 x+24$
• $y^2=107 x^6+26 x^5+107 x^4+61 x^3+94 x^2+2 x+93$
• $y^2=110 x^6+69 x^5+26 x^4+40 x^3+65 x^2+10 x+59$
• $y^2=6 x^6+70 x^5+30 x^4+26 x^3+96 x^2+42 x+51$
• $y^2=40 x^6+104 x^5+20 x^4+36 x^3+49 x^2+7 x+15$
• $y^2=48 x^6+57 x^5+46 x^4+104 x^3+96 x^2+67 x+36$
• $y^2=28 x^6+104 x^5+25 x^4+111 x^3+23 x^2+66 x+89$
• $y^2=86 x^6+110 x^5+26 x^4+39 x^3+4 x^2+68 x+23$
• $y^2=63 x^6+102 x^5+61 x^4+13 x^3+30 x^2+27 x+90$
• $y^2=72 x^6+30 x^5+27 x^4+78 x^3+46 x^2+38 x+94$
• $y^2=92 x^6+27 x^5+89 x^4+108 x^3+11 x^2+50 x+16$
• $y^2=31 x^6+79 x^5+3 x^4+63 x^3+33 x^2+43 x+4$
• $y^2=27 x^6+88 x^5+27 x^4+51 x^3+12 x^2+55 x+53$
• $y^2=103 x^6+52 x^5+x^4+15 x^3+46 x^2+94 x+36$
• $y^2=109 x^6+5 x^5+18 x^4+59 x^3+42 x^2+34 x+71$
• $y^2=104 x^6+83 x^5+12 x^4+55 x^3+70 x^2+106 x+40$
• $y^2=47 x^6+109 x^5+23 x^4+36 x^3+45 x^2+43$
• $y^2=105 x^6+56 x^5+69 x^4+28 x^3+39 x^2+x+34$
• $y^2=105 x^6+30 x^5+37 x^4+86 x^3+79 x^2+39 x+81$
• $y^2=12 x^6+50 x^5+50 x^4+x^3+13 x^2+9 x+64$
• $y^2=107 x^6+21 x^5+51 x^4+16 x^3+36 x^2+42 x+24$
• $y^2=63 x^6+58 x^5+42 x^4+106 x^3+14 x+10$
• $y^2=99 x^6+11 x^5+32 x^4+5 x^3+110 x^2+93 x+3$
• $y^2=94 x^6+61 x^5+90 x^4+86 x^3+99 x^2+x+34$
• $y^2=91 x^6+x^5+109 x^4+63 x^3+73 x^2+25 x+23$
• $y^2=33 x^6+8 x^5+16 x^4+37 x^3+82 x^2+9 x+48$
• $y^2=31 x^6+5 x^5+89 x^4+4 x^3+84 x^2+2 x+5$
• $y^2=13 x^6+69 x^5+30 x^4+82 x^3+42 x^2+74 x+94$
• $y^2=43 x^6+15 x^5+17 x^4+49 x^3+50 x^2+26$
• $y^2=103 x^6+31 x^5+27 x^4+4 x^3+73 x^2+107 x+94$
• $y^2=88 x^6+106 x^5+68 x^4+72 x^3+72 x^2+109 x+92$
• $y^2=35 x^6+83 x^5+89 x^4+16 x^3+6 x^2+6 x+2$
• $y^2=6 x^6+18 x^5+8 x^4+90 x^3+82 x^2+105 x+38$
• $y^2=87 x^6+22 x^5+21 x^4+7 x^3+75 x^2+46 x+29$
• $y^2=31 x^6+11 x^5+92 x^4+3 x^3+101 x^2+7 x+59$
• $y^2=17 x^6+30 x^5+91 x^4+95 x^3+58 x^2+10 x+68$
• $y^2=103 x^6+34 x^5+92 x^4+17 x^3+53 x^2+x+57$
• $y^2=10 x^6+87 x^5+72 x^4+59 x^3+31 x^2+72 x+46$
• $y^2=81 x^6+48 x^5+87 x^4+x^3+32 x^2+105 x+10$
• $y^2=71 x^6+105 x^5+90 x^4+32 x^3+39 x^2+81 x+58$
• $y^2=98 x^6+66 x^5+15 x^4+95 x^3+73 x^2+94 x+42$
• $y^2=9 x^6+7 x^5+107 x^4+26 x^3+5 x^2+75 x+61$
• $y^2=98 x^6+71 x^5+106 x^4+36 x^3+66 x^2+2 x+50$
• $y^2=46 x^6+45 x^5+10 x^4+102 x^3+6 x^2+33 x+40$

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 4.0.2697017616.1.

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.u_ih	$2$	(not in LMFDB)