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

• Label: 2.113.abb_po
• 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:	$1 - 27 x + 404 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.238608637507$, $\pm0.319172747552$
Angle rank:	$2$ (numerical)
Number field:	4.0.3757.1
Galois group:	$D_{4}$
Jacobians:	$72$
Isomorphism classes:	72

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10096$	$164080192$	$2087568213952$	$26591251366566144$	$339459365089242708976$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12849$	$1446786$	$163089121$	$18424494327$	$2081949583902$	$235260509667207$	$26584441670674369$	$3004041938075562402$	$339456739009678938609$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=70 x^6+68 x^5+77 x^4+53 x^3+38 x^2+37 x+23$
• $y^2=15 x^6+88 x^4+39 x^3+95 x^2+47 x+96$
• $y^2=83 x^6+82 x^5+40 x^4+90 x^3+88 x^2+7 x+81$
• $y^2=52 x^6+14 x^5+41 x^4+37 x^3+101 x^2+30 x+76$
• $y^2=105 x^6+14 x^5+65 x^4+81 x^3+38 x^2+36 x+108$
• $y^2=51 x^6+84 x^5+19 x^4+71 x^3+45 x^2+77 x+94$
• $y^2=18 x^6+53 x^5+102 x^4+72 x^3+95 x^2+6 x+63$
• $y^2=83 x^6+18 x^5+68 x^4+24 x^3+70 x^2+62 x+18$
• $y^2=74 x^6+74 x^5+42 x^4+34 x^3+x^2+56 x+31$
• $y^2=29 x^6+111 x^5+63 x^4+88 x^3+10 x^2+22 x+7$
• $y^2=59 x^6+10 x^5+82 x^4+52 x^3+44 x^2+78 x+36$
• $y^2=38 x^6+60 x^5+82 x^4+76 x^3+20 x^2+3 x+93$
• $y^2=38 x^6+16 x^5+29 x^4+20 x^3+35 x^2+81 x+93$
• $y^2=86 x^6+20 x^5+90 x^4+51 x^3+102 x^2+90 x+67$
• $y^2=16 x^6+x^5+54 x^4+16 x^3+19 x^2+95 x+99$
• $y^2=61 x^6+79 x^5+78 x^4+97 x^3+76 x^2+33 x+104$
• $y^2=22 x^6+101 x^5+93 x^4+72 x^3+67 x^2+36 x+81$
• $y^2=89 x^6+65 x^5+102 x^4+98 x^3+19 x^2+74 x+108$
• $y^2=71 x^6+105 x^5+22 x^4+76 x^3+31 x^2+2 x+39$
• $y^2=48 x^6+48 x^5+45 x^4+101 x^3+21 x^2+105 x+31$
• and

• $y^2=61 x^6+109 x^5+41 x^4+31 x^3+85 x^2+65 x+65$
• $y^2=90 x^6+12 x^5+37 x^4+65 x^3+23 x^2+99 x+42$
• $y^2=13 x^6+38 x^5+82 x^4+5 x^3+51 x+5$
• $y^2=55 x^6+6 x^5+17 x^4+37 x^3+43 x^2+53 x+84$
• $y^2=28 x^6+48 x^5+92 x^4+16 x^3+80 x^2+7 x+68$
• $y^2=43 x^6+98 x^5+19 x^4+83 x^3+4 x^2+61 x+58$
• $y^2=64 x^6+17 x^5+18 x^4+63 x^3+53 x^2+56 x+11$
• $y^2=92 x^6+11 x^5+51 x^4+79 x^3+55 x^2+106 x+45$
• $y^2=12 x^6+110 x^5+108 x^4+85 x^3+98 x^2+56 x+90$
• $y^2=45 x^6+91 x^5+26 x^4+89 x^3+54 x^2+x+70$
• $y^2=15 x^6+99 x^5+3 x^4+13 x^3+88 x^2+34 x+101$
• $y^2=42 x^6+32 x^5+57 x^4+85 x^3+31 x^2+59 x+58$
• $y^2=57 x^6+6 x^5+55 x^4+85 x^3+73 x^2+100 x+100$
• $y^2=3 x^6+48 x^5+79 x^4+108 x^3+25 x^2+58 x+73$
• $y^2=15 x^6+68 x^5+48 x^4+3 x^3+66 x^2+110 x+110$
• $y^2=12 x^6+13 x^5+40 x^4+95 x^3+26 x^2+25 x+80$
• $y^2=84 x^6+51 x^5+97 x^4+61 x^3+19 x^2+13 x+11$
• $y^2=91 x^6+56 x^5+42 x^4+51 x^3+18 x^2+95 x+58$
• $y^2=109 x^6+94 x^5+92 x^4+6 x^3+63 x^2+72 x+108$
• $y^2=27 x^6+90 x^5+48 x^4+31 x^3+39 x^2+33 x+45$
• $y^2=69 x^6+86 x^5+47 x^4+53 x^3+20 x^2+84 x+60$
• $y^2=77 x^5+51 x^4+82 x^3+9 x^2+64 x+106$
• $y^2=58 x^6+10 x^5+31 x^4+40 x^3+40 x^2+66 x+69$
• $y^2=38 x^6+32 x^5+98 x^4+39 x^3+76 x^2+24 x+90$
• $y^2=112 x^6+70 x^5+21 x^4+51 x^3+87 x^2+22 x+78$
• $y^2=19 x^6+4 x^5+86 x^4+82 x^3+107 x^2+19 x+12$
• $y^2=17 x^6+44 x^5+62 x^4+35 x^3+13 x^2+92 x+50$
• $y^2=37 x^6+101 x^5+56 x^4+98 x^3+83 x^2+70 x+45$
• $y^2=14 x^6+36 x^5+8 x^4+64 x^3+33 x^2+106 x+86$
• $y^2=23 x^6+47 x^5+112 x^4+32 x^3+27 x^2+3 x+92$
• $y^2=78 x^6+63 x^5+106 x^4+38 x^3+81 x^2+52 x+65$
• $y^2=12 x^6+73 x^5+35 x^4+98 x^3+19 x^2+2 x+17$
• $y^2=40 x^6+34 x^5+26 x^4+37 x^3+25 x+105$
• $y^2=6 x^6+53 x^5+96 x^4+20 x^3+111 x^2+97 x+103$
• $y^2=48 x^6+98 x^5+31 x^4+56 x^3+38 x^2+4 x+98$
• $y^2=31 x^6+9 x^5+97 x^4+45 x^3+30 x^2+54 x+109$
• $y^2=6 x^6+85 x^5+100 x^4+41 x^3+28 x^2+57 x+100$
• $y^2=91 x^6+4 x^5+65 x^4+34 x^3+64 x^2+88 x+79$
• $y^2=70 x^6+62 x^5+22 x^4+63 x^3+3 x^2+78 x+12$
• $y^2=94 x^6+73 x^5+72 x^4+66 x^3+84 x^2+108 x+68$
• $y^2=57 x^6+92 x^5+20 x^4+11 x^3+34 x^2+39 x+76$
• $y^2=33 x^6+11 x^5+2 x^4+91 x^3+x^2+51 x+42$
• $y^2=91 x^6+48 x^5+7 x^4+57 x^3+81 x^2+58 x+62$
• $y^2=10 x^6+105 x^5+84 x^4+43 x^3+22 x^2+50 x+49$
• $y^2=23 x^6+77 x^5+28 x^4+53 x^3+17 x^2+82 x+14$
• $y^2=57 x^6+43 x^5+105 x^4+84 x^3+69 x^2+91 x+45$
• $y^2=51 x^6+67 x^4+20 x^3+53 x^2+64 x+26$
• $y^2=57 x^6+101 x^5+19 x^4+112 x^2+42 x+62$
• $y^2=86 x^6+56 x^5+51 x^4+101 x^3+75 x^2+33 x+47$
• $y^2=30 x^6+85 x^5+110 x^4+110 x^3+55 x^2+84 x+102$
• $y^2=72 x^6+17 x^5+36 x^4+13 x^3+54 x^2+85 x+24$
• $y^2=39 x^6+31 x^5+60 x^4+6 x^3+81 x^2+24 x+4$

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 4.0.3757.1.

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_po	$2$	(not in LMFDB)