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

• Label: 2.113.av_iq
• 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:	$1 - 21 x + 224 x^{2} - 2373 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0397408763992$, $\pm0.501419504344$
Angle rank:	$2$ (numerical)
Number field:	4.0.159667992.1
Galois group:	$D_{4}$
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10600$	$163112800$	$2078682217600$	$26576624217456000$	$339452792144672113000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$12777$	$1440630$	$162999409$	$18424137573$	$2081952524094$	$235260527399109$	$26584441426657441$	$3004041936624482070$	$339456739017362599257$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=29 x^6+64 x^5+23 x^3+98 x^2+54 x+21$
• $y^2=96 x^6+106 x^5+50 x^4+51 x^3+x^2+50 x+27$
• $y^2=57 x^6+38 x^5+63 x^4+104 x^3+26 x^2+5 x+29$
• $y^2=8 x^6+83 x^5+55 x^4+109 x^3+38 x^2+32 x+100$
• $y^2=38 x^6+111 x^5+21 x^4+58 x^3+56 x^2+27 x+103$
• $y^2=3 x^6+54 x^5+65 x^4+53 x^3+110 x^2+106 x+5$
• $y^2=58 x^6+79 x^5+108 x^4+8 x^3+6 x^2+100 x+15$
• $y^2=31 x^6+106 x^5+17 x^4+43 x^3+84 x^2+59 x+33$
• $y^2=67 x^6+85 x^5+108 x^4+64 x^3+91 x^2+74 x+12$
• $y^2=38 x^6+22 x^5+22 x^4+88 x^3+78 x^2+69 x+85$
• $y^2=20 x^6+88 x^5+35 x^4+101 x^3+77 x^2+28 x+89$
• $y^2=28 x^6+x^5+81 x^4+74 x^3+109 x^2+95 x+14$
• $y^2=71 x^6+88 x^5+105 x^4+19 x^3+40 x^2+57 x+91$
• $y^2=40 x^6+30 x^5+92 x^4+100 x^3+68 x^2+38 x+17$
• $y^2=67 x^6+47 x^5+76 x^4+55 x^3+70 x^2+56 x+60$
• $y^2=41 x^6+76 x^5+97 x^4+46 x^3+69 x^2+68 x+48$
• $y^2=31 x^6+2 x^5+63 x^4+40 x^3+69 x^2+81 x+36$
• $y^2=51 x^6+102 x^5+13 x^4+82 x^3+111 x^2+79 x+1$
• $y^2=6 x^6+47 x^5+104 x^4+111 x^3+2 x^2+83 x+35$
• $y^2=79 x^6+24 x^5+111 x^4+68 x^3+58 x^2+19 x+64$
• and

• $y^2=101 x^6+18 x^5+76 x^4+8 x^3+4 x^2+47 x+81$
• $y^2=10 x^6+63 x^5+73 x^4+61 x^3+x^2+20 x+18$
• $y^2=49 x^6+78 x^5+60 x^4+52 x^3+7 x+76$
• $y^2=19 x^6+77 x^5+108 x^4+36 x^3+91 x^2+44 x+19$
• $y^2=43 x^6+41 x^5+25 x^4+96 x^3+101 x^2+21 x+85$
• $y^2=77 x^6+20 x^5+94 x^4+49 x^3+83 x^2+70 x+71$
• $y^2=90 x^6+6 x^5+99 x^4+44 x^3+110 x^2+68 x+11$
• $y^2=78 x^6+45 x^5+56 x^4+41 x^3+16 x^2+28 x+87$
• $y^2=20 x^6+2 x^5+59 x^4+85 x^3+61 x^2+45 x+24$
• $y^2=92 x^6+107 x^5+32 x^4+56 x^3+17 x^2+23 x+23$
• $y^2=76 x^6+62 x^5+65 x^4+36 x^3+79 x^2+100 x+56$
• $y^2=112 x^6+40 x^5+28 x^4+7 x^3+20 x^2+52 x+6$
• $y^2=76 x^6+18 x^5+68 x^4+55 x^3+39 x+11$
• $y^2=27 x^6+43 x^5+16 x^4+49 x^3+36 x^2+72 x+38$
• $y^2=6 x^6+105 x^5+108 x^4+95 x^3+52 x^2+36 x+15$
• $y^2=48 x^6+30 x^5+39 x^4+83 x^3+33 x^2+60 x+102$
• $y^2=21 x^6+93 x^5+90 x^4+28 x^3+51 x^2+77 x+97$
• $y^2=78 x^6+12 x^5+23 x^4+7 x^3+15 x^2+68 x+57$
• $y^2=97 x^6+45 x^5+61 x^4+69 x^3+7 x^2+47 x$
• $y^2=78 x^6+74 x^5+90 x^4+21 x^3+15 x^2+77 x+42$
• $y^2=92 x^6+20 x^5+109 x^4+31 x^3+58 x^2+69 x+9$
• $y^2=110 x^6+43 x^5+89 x^4+32 x^3+13 x^2+96 x+12$
• $y^2=77 x^6+48 x^5+26 x^4+81 x^3+85 x^2+x+105$
• $y^2=75 x^6+112 x^5+72 x^4+51 x^3+34 x^2+35 x+63$
• $y^2=53 x^6+40 x^5+84 x^4+62 x^3+19 x^2+52 x+92$
• $y^2=88 x^6+12 x^5+70 x^4+91 x^3+97 x^2+100 x+106$
• $y^2=26 x^6+47 x^5+96 x^4+65 x^3+102 x^2+64 x+33$
• $y^2=19 x^6+48 x^5+44 x^4+48 x^3+100 x^2+64 x+84$

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 4.0.159667992.1.

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.v_iq	$2$	(not in LMFDB)