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

• Label: 2.113.abi_tk
• 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:	$1 - 34 x + 504 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0951939817064$, $\pm0.277435139411$
Angle rank:	$2$ (numerical)
Number field:	4.0.410432.1
Galois group:	$D_{4}$
Jacobians:	$42$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9398$	$161175700$	$2082785521238$	$26586837522434000$	$339458097749389271398$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$12622$	$1443476$	$163062054$	$18424425540$	$2081950965694$	$235260533187872$	$26584441916263806$	$3004041941071957568$	$339456739056622954782$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=49 x^6+95 x^5+8 x^4+88 x^3+16 x^2+68 x+105$
• $y^2=35 x^6+43 x^5+13 x^4+5 x^3+100 x^2+101 x+108$
• $y^2=2 x^6+88 x^5+96 x^4+6 x^3+35 x^2+101 x+89$
• $y^2=65 x^6+73 x^5+84 x^4+34 x^3+30 x^2+84$
• $y^2=59 x^6+43 x^5+36 x^4+110 x^3+63 x^2+104 x+10$
• $y^2=55 x^6+16 x^5+66 x^4+55 x^3+68 x^2+111 x+69$
• $y^2=79 x^6+24 x^5+36 x^4+41 x^3+90 x^2+21 x+17$
• $y^2=44 x^6+47 x^5+98 x^4+106 x^3+16 x^2+20 x+10$
• $y^2=47 x^6+95 x^5+97 x^4+78 x^3+57 x^2+25 x+38$
• $y^2=7 x^6+77 x^5+54 x^4+43 x^3+14 x^2+69 x+83$
• $y^2=52 x^6+108 x^5+89 x^4+31 x^3+63 x^2+79 x+33$
• $y^2=34 x^6+99 x^5+41 x^4+27 x^3+60 x^2+66 x+86$
• $y^2=75 x^6+84 x^5+12 x^4+54 x^3+40 x^2+19 x+7$
• $y^2=9 x^6+x^5+101 x^4+4 x^3+52 x^2+58 x+39$
• $y^2=29 x^5+14 x^4+22 x^3+82 x^2+8 x+3$
• $y^2=81 x^6+63 x^5+26 x^4+93 x^3+112 x^2+101 x+95$
• $y^2=89 x^6+76 x^5+45 x^4+99 x^3+84 x^2+42 x+71$
• $y^2=65 x^6+26 x^5+76 x^4+75 x^3+66 x^2+23 x+90$
• $y^2=84 x^6+11 x^5+93 x^4+91 x^3+56 x^2+34 x+10$
• $y^2=111 x^6+11 x^5+17 x^4+23 x^3+56 x^2+77 x+75$
• and

• $y^2=23 x^6+89 x^5+70 x^4+33 x^3+101 x^2+100 x+55$
• $y^2=38 x^6+10 x^5+3 x^4+2 x^3+13 x^2+11 x+96$
• $y^2=80 x^6+39 x^5+13 x^4+2 x^3+55 x^2+4 x+107$
• $y^2=33 x^6+49 x^5+20 x^4+56 x^3+32 x^2+45 x+52$
• $y^2=78 x^6+15 x^5+110 x^4+53 x^3+9 x^2+3 x+106$
• $y^2=73 x^6+78 x^5+84 x^4+42 x^3+45 x^2+43 x+55$
• $y^2=77 x^6+106 x^5+41 x^4+7 x^3+53 x^2+56 x+103$
• $y^2=105 x^6+101 x^5+73 x^4+27 x^3+13 x^2+77 x+90$
• $y^2=101 x^6+32 x^5+62 x^4+71 x^3+49 x^2+79 x+5$
• $y^2=74 x^6+x^5+60 x^4+77 x^3+40 x^2+69 x+88$
• $y^2=40 x^6+84 x^5+22 x^4+52 x^3+53 x^2+x+77$
• $y^2=10 x^6+8 x^5+73 x^4+99 x^3+15 x^2+21 x+55$
• $y^2=108 x^6+90 x^5+15 x^4+77 x^3+75 x^2+86 x+50$
• $y^2=20 x^6+62 x^5+107 x^4+93 x^3+73 x^2+95 x+15$
• $y^2=95 x^6+57 x^5+29 x^4+25 x^3+38 x^2+96 x+70$
• $y^2=82 x^6+26 x^5+36 x^4+11 x^3+69 x^2+30 x+54$
• $y^2=105 x^6+88 x^5+39 x^4+29 x^3+15 x^2+51 x+1$
• $y^2=38 x^6+109 x^5+55 x^4+68 x^3+109 x^2+62$
• $y^2=93 x^6+58 x^5+96 x^4+43 x^3+111 x^2+96 x+89$
• $y^2=10 x^6+11 x^5+49 x^4+64 x^3+104 x^2+59 x+5$
• $y^2=88 x^6+62 x^5+37 x^4+55 x^3+30 x^2+96 x+24$
• $y^2=91 x^6+108 x^5+48 x^4+98 x^3+63 x^2+81 x+57$

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 4.0.410432.1.

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.bi_tk	$2$	(not in LMFDB)