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

• Label: 2.113.abe_qu
• 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:	$1 - 30 x + 436 x^{2} - 3390 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.152294777786$, $\pm0.324674258262$
Angle rank:	$2$ (numerical)
Number field:	4.0.113198400.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9786$	$162702036$	$2084940660474$	$26588303998529616$	$339458510510103231786$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$12742$	$1444968$	$163071046$	$18424447944$	$2081951685718$	$235260557973588$	$26584442279619838$	$3004041942717486804$	$339456739015889340022$

Jacobians and polarizations

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

• $y^2=28 x^6+82 x^5+26 x^4+63 x^3+77 x^2+98 x+93$
• $y^2=21 x^6+74 x^5+60 x^4+79 x^3+27 x^2+81 x+3$
• $y^2=43 x^6+35 x^5+x^4+100 x^3+89 x^2+87 x+1$
• $y^2=87 x^6+112 x^5+44 x^4+110 x^3+90 x^2+14 x+94$
• $y^2=41 x^6+45 x^5+35 x^4+19 x^3+68 x^2+46 x+79$
• $y^2=41 x^6+25 x^5+79 x^4+51 x^3+66 x^2+11 x+103$
• $y^2=42 x^6+60 x^5+7 x^4+28 x^3+85 x^2+4 x+93$
• $y^2=6 x^6+97 x^5+42 x^4+19 x^3+24 x^2+47 x+34$
• $y^2=108 x^6+86 x^5+36 x^4+57 x^3+50 x^2+47 x+11$
• $y^2=112 x^6+32 x^5+3 x^4+36 x^3+80 x^2+77 x+52$
• $y^2=77 x^6+101 x^5+33 x^4+80 x^3+41 x^2+47 x+67$
• $y^2=76 x^6+85 x^5+25 x^4+12 x^3+74 x^2+4 x+79$
• $y^2=69 x^6+96 x^5+63 x^4+53 x^3+34 x^2+88 x+84$
• $y^2=74 x^6+92 x^5+9 x^4+60 x^3+41 x^2+39 x+30$
• $y^2=88 x^6+91 x^5+75 x^4+99 x^3+45 x^2+62 x+38$
• $y^2=108 x^6+111 x^5+77 x^4+17 x^3+75 x^2+9 x+89$
• $y^2=77 x^6+102 x^5+92 x^4+93 x^3+32 x^2+70 x+39$
• $y^2=72 x^6+77 x^5+42 x^4+24 x^3+26 x^2+74 x+73$
• $y^2=69 x^6+51 x^5+100 x^4+48 x^3+25 x^2+22 x$
• $y^2=54 x^6+12 x^5+53 x^4+94 x^3+66 x^2+81 x+16$
• and

• $y^2=88 x^6+78 x^5+7 x^4+80 x^3+112 x^2+24 x+42$
• $y^2=46 x^6+95 x^5+56 x^4+4 x^3+x^2+102 x+88$
• $y^2=96 x^6+104 x^5+41 x^4+55 x^3+47 x^2+21 x+5$
• $y^2=40 x^6+111 x^5+39 x^4+11 x^3+78 x^2+79 x+86$
• $y^2=10 x^6+57 x^5+57 x^4+65 x^3+57 x^2+104 x+82$
• $y^2=10 x^6+57 x^5+47 x^4+33 x^3+92 x^2+38 x+14$
• $y^2=21 x^6+22 x^5+26 x^4+80 x^3+56 x^2+110 x+13$
• $y^2=21 x^6+63 x^5+37 x^4+76 x^3+60 x^2+85 x+88$
• $y^2=18 x^6+44 x^5+107 x^4+101 x^3+97 x^2+69 x+77$
• $y^2=98 x^6+70 x^5+94 x^4+73 x^3+92 x^2+42 x+17$
• $y^2=108 x^6+84 x^5+31 x^4+68 x^3+98 x^2+2 x+58$
• $y^2=95 x^6+41 x^5+19 x^4+11 x^3+85 x^2+77 x+90$
• $y^2=101 x^6+46 x^5+67 x^4+60 x^3+61 x^2+44 x+81$
• $y^2=11 x^6+93 x^5+3 x^4+15 x^3+5 x^2+70 x+5$
• $y^2=102 x^6+19 x^5+21 x^4+100 x^3+70 x^2+56 x+79$
• $y^2=38 x^6+106 x^5+37 x^4+9 x^3+102 x^2+32 x+83$
• $y^2=78 x^6+47 x^5+57 x^4+18 x^3+91 x^2+43 x+96$
• $y^2=62 x^6+25 x^5+26 x^4+95 x^3+112 x^2+93 x+84$
• $y^2=60 x^6+68 x^5+34 x^4+37 x^3+71 x^2+55 x+60$
• $y^2=56 x^6+70 x^5+76 x^4+37 x^3+49 x^2+97 x+23$
• $y^2=19 x^6+31 x^5+76 x^4+57 x^3+29 x^2+91 x+111$
• $y^2=86 x^6+14 x^5+43 x^4+20 x^3+54 x^2+33 x+70$
• $y^2=82 x^6+102 x^5+93 x^4+11 x^3+66 x^2+14 x+68$
• $y^2=61 x^6+79 x^5+38 x^4+5 x^3+15 x^2+17 x+58$
• $y^2=9 x^6+73 x^5+40 x^4+30 x^3+110 x^2+49 x+25$
• $y^2=11 x^6+2 x^5+5 x^4+100 x^3+112 x^2+51 x+26$
• $y^2=23 x^6+4 x^5+39 x^4+72 x^3+101 x^2+112 x+8$
• $y^2=110 x^6+56 x^5+26 x^4+21 x^3+49 x^2+9 x+21$
• $y^2=47 x^6+17 x^5+111 x^4+13 x^3+108 x^2+92 x+29$
• $y^2=76 x^6+44 x^5+98 x^4+27 x^3+17 x^2+104 x+59$
• $y^2=15 x^6+90 x^5+77 x^4+106 x^3+84 x^2+79 x+80$
• $y^2=34 x^6+60 x^5+68 x^4+101 x^3+65 x^2+19 x+92$
• $y^2=16 x^6+29 x^5+46 x^4+90 x^3+91 x^2+74 x+24$
• $y^2=7 x^6+40 x^5+63 x^4+12 x^3+100 x^2+93 x+88$
• $y^2=38 x^6+106 x^5+35 x^4+90 x^3+58 x^2+33 x+24$
• $y^2=84 x^6+70 x^5+49 x^4+111 x^3+77 x^2+102 x+106$
• $y^2=35 x^6+x^5+36 x^4+19 x^3+86 x^2+107 x+4$
• $y^2=58 x^6+52 x^5+93 x^4+53 x^3+6 x^2+7 x+2$
• $y^2=26 x^6+96 x^5+23 x^4+13 x^3+61 x^2+93 x+71$
• $y^2=82 x^6+98 x^5+56 x^4+88 x^3+105 x^2+65 x+42$
• $y^2=55 x^6+6 x^5+65 x^4+84 x^3+70 x^2+111 x+66$
• $y^2=5 x^6+21 x^5+74 x^4+14 x^3+43 x^2+101 x+23$
• $y^2=98 x^6+68 x^5+46 x^4+92 x^3+48 x^2+62 x+9$
• $y^2=5 x^6+101 x^5+98 x^4+63 x^3+105 x^2+103 x+4$
• $y^2=95 x^6+9 x^5+35 x^4+23 x^3+26 x^2+33 x+73$
• $y^2=40 x^6+30 x^5+45 x^4+42 x^3+21 x^2+47 x+58$
• $y^2=92 x^6+27 x^5+6 x^4+33 x^3+95 x^2+100 x+26$
• $y^2=70 x^6+47 x^5+112 x^4+112 x^3+31 x^2+23 x+83$

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 4.0.113198400.1.

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.be_qu	$2$	(not in LMFDB)