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

• Label: 2.113.abb_pn
• 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:	$1 - 27 x + 403 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.233516481182$, $\pm0.323236817002$
Angle rank:	$2$ (numerical)
Number field:	4.0.29164653.1
Galois group:	$D_{4}$
Jacobians:	$66$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10095$	$164053845$	$2087451136215$	$26591039048783925$	$339459278029398927600$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12847$	$1446705$	$163087819$	$18424489602$	$2081949801199$	$235260514642821$	$26584441717485811$	$3004041938019227955$	$339456739001440440382$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 66 curves (of which all are hyperelliptic):

• $y^2=60 x^6+97 x^5+10 x^4+15 x^3+86 x^2+58 x+50$
• $y^2=12 x^6+97 x^5+4 x^4+39 x^3+6 x^2+62 x+4$
• $y^2=60 x^6+39 x^5+13 x^4+100 x^3+90 x^2+89 x+28$
• $y^2=13 x^6+81 x^5+108 x^4+86 x^3+28 x^2+54 x+37$
• $y^2=29 x^6+56 x^5+57 x^4+80 x^3+34 x^2+17$
• $y^2=73 x^6+50 x^5+21 x^4+105 x^3+48 x^2+59 x+45$
• $y^2=54 x^6+68 x^5+75 x^4+75 x^2+97 x+62$
• $y^2=96 x^6+33 x^5+18 x^4+3 x^3+74 x^2+34 x+100$
• $y^2=3 x^6+85 x^5+8 x^4+112 x^3+54 x^2+6 x+13$
• $y^2=49 x^6+27 x^5+20 x^4+29 x^3+80 x^2+33 x+84$
• $y^2=77 x^6+23 x^5+9 x^4+14 x^3+86 x^2+91 x+66$
• $y^2=26 x^6+64 x^5+98 x^4+112 x^3+42 x^2+42 x+40$
• $y^2=33 x^6+42 x^5+46 x^4+74 x^3+15 x^2+48 x+51$
• $y^2=26 x^6+91 x^5+98 x^4+8 x^3+36 x^2+39 x+18$
• $y^2=20 x^6+55 x^5+25 x^4+100 x^3+18 x^2+72 x+94$
• $y^2=72 x^6+22 x^5+22 x^4+52 x^3+39 x^2+43 x+99$
• $y^2=73 x^6+74 x^5+51 x^4+110 x^3+36 x^2+29 x+13$
• $y^2=104 x^6+57 x^5+23 x^4+91 x^3+7 x^2+74 x+53$
• $y^2=100 x^6+36 x^5+30 x^4+18 x^3+33 x^2+10 x+22$
• $y^2=2 x^6+99 x^5+85 x^4+81 x^3+8 x^2+34 x+3$
• and

• $y^2=101 x^6+102 x^5+7 x^4+x^3+27 x^2+55 x+107$
• $y^2=2 x^6+97 x^5+43 x^4+70 x^3+101 x^2+9 x+76$
• $y^2=44 x^6+6 x^5+54 x^4+37 x^3+92 x^2+71 x+31$
• $y^2=73 x^6+76 x^5+48 x^4+60 x^3+37 x^2+18 x+70$
• $y^2=23 x^6+27 x^5+47 x^4+20 x^3+41 x^2+9 x+92$
• $y^2=70 x^6+26 x^5+4 x^4+16 x^3+110 x^2+70 x+66$
• $y^2=66 x^6+13 x^5+74 x^4+15 x^3+8 x^2+17 x+22$
• $y^2=84 x^6+18 x^5+11 x^3+110 x^2+83 x+80$
• $y^2=31 x^6+74 x^5+77 x^4+89 x^3+26 x^2+28 x+103$
• $y^2=6 x^6+79 x^5+77 x^4+46 x^3+93 x^2+20 x+28$
• $y^2=9 x^6+14 x^5+59 x^4+68 x^3+70 x^2+21 x+83$
• $y^2=46 x^6+106 x^5+63 x^4+101 x^3+24 x^2+45 x+6$
• $y^2=69 x^6+65 x^5+61 x^4+43 x^3+54 x^2+71 x+28$
• $y^2=21 x^6+61 x^5+95 x^4+40 x^3+50 x^2+27 x+12$
• $y^2=101 x^6+36 x^5+15 x^4+63 x^3+28 x^2+23 x+17$
• $y^2=35 x^6+25 x^5+15 x^4+70 x^3+96 x^2+71 x+28$
• $y^2=88 x^6+109 x^5+78 x^4+27 x^3+35 x^2+54 x+88$
• $y^2=96 x^6+20 x^5+74 x^4+89 x^3+68 x^2+93 x+99$
• $y^2=91 x^6+93 x^5+6 x^4+4 x^3+96 x^2+59 x+105$
• $y^2=56 x^6+28 x^5+64 x^4+25 x^3+75 x^2+96 x+42$
• $y^2=3 x^6+79 x^5+57 x^4+22 x^3+2 x^2+11 x+86$
• $y^2=73 x^6+69 x^5+112 x^4+11 x^3+106 x^2+58 x+111$
• $y^2=78 x^6+24 x^5+x^4+18 x^3+100 x^2+24 x+33$
• $y^2=34 x^6+98 x^5+107 x^4+26 x^3+55 x^2+103 x+41$
• $y^2=52 x^6+97 x^5+74 x^4+105 x^3+24 x^2+25 x+80$
• $y^2=67 x^6+54 x^5+67 x^3+23 x^2+78 x+103$
• $y^2=95 x^6+3 x^5+72 x^4+49 x^3+94 x^2+19 x+31$
• $y^2=6 x^6+25 x^5+112 x^4+15 x^3+88 x^2+56 x+73$
• $y^2=60 x^6+59 x^5+69 x^4+61 x^3+26 x^2+41 x+26$
• $y^2=89 x^6+110 x^5+91 x^4+68 x^3+69 x^2+30 x+84$
• $y^2=49 x^6+56 x^5+8 x^4+98 x^3+2 x^2+61 x+57$
• $y^2=29 x^6+79 x^5+49 x^4+55 x^3+44 x^2+18 x+69$
• $y^2=9 x^6+31 x^5+79 x^4+40 x^3+49 x^2+51 x+99$
• $y^2=8 x^6+47 x^5+38 x^4+103 x^3+93 x^2+74 x+6$
• $y^2=51 x^6+44 x^5+96 x^4+43 x^3+83 x^2+72 x+8$
• $y^2=54 x^6+63 x^5+82 x^4+18 x^3+110 x^2+64 x+90$
• $y^2=108 x^6+105 x^5+81 x^4+64 x^3+71 x^2+61 x+5$
• $y^2=40 x^6+34 x^5+81 x^4+41 x^3+58 x^2+76 x+74$
• $y^2=94 x^6+49 x^4+23 x^3+95 x^2+36 x+70$
• $y^2=105 x^6+47 x^5+44 x^4+36 x^3+68 x^2+64 x+105$
• $y^2=47 x^6+74 x^5+81 x^4+42 x^3+7 x^2+75 x+1$
• $y^2=5 x^6+101 x^5+60 x^4+86 x^3+55 x^2+52 x+99$
• $y^2=5 x^6+65 x^5+95 x^4+18 x^3+40 x^2+101$
• $y^2=89 x^6+65 x^5+30 x^4+47 x^3+52 x^2+51 x+20$
• $y^2=48 x^6+108 x^5+77 x^4+48 x^3+41 x^2+63 x+20$
• $y^2=89 x^6+83 x^5+25 x^4+47 x^3+26 x^2+3 x+80$

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 4.0.29164653.1.

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.bb_pn	$2$	(not in LMFDB)