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

• Label: 2.113.aba_pa
• 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:	$1 - 26 x + 390 x^{2} - 2938 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.245677096695$, $\pm0.331015515338$
Angle rank:	$2$ (numerical)
Number field:	4.0.1847600.2
Galois group:	$D_{4}$
Jacobians:	$72$
Isomorphism classes:	96

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10196$	$164400304$	$2087773427924$	$26590786443819776$	$339458166042819831316$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$12874$	$1446928$	$163086270$	$18424429248$	$2081949104458$	$235260511838440$	$26584441751221374$	$3004041938711558344$	$339456739007930520714$

Jacobians and polarizations

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

• $y^2=75 x^6+107 x^5+107 x^4+67 x^3+16 x^2+80 x+13$
• $y^2=65 x^6+6 x^5+20 x^4+9 x^3+77 x^2+x+3$
• $y^2=48 x^6+59 x^5+88 x^4+42 x^3+77 x^2+86 x+54$
• $y^2=11 x^6+31 x^5+63 x^4+98 x^3+11 x^2+19 x+35$
• $y^2=45 x^6+52 x^5+26 x^4+22 x^3+72 x^2+21 x+82$
• $y^2=x^6+90 x^5+18 x^4+52 x^3+72 x^2+x+60$
• $y^2=82 x^6+55 x^5+94 x^4+99 x^3+47 x^2+32 x+71$
• $y^2=32 x^6+12 x^5+2 x^4+16 x^3+93 x^2+68 x+46$
• $y^2=39 x^6+44 x^5+8 x^4+100 x^3+14 x^2+76 x+25$
• $y^2=45 x^6+66 x^5+111 x^4+78 x^3+34 x^2+101 x+94$
• $y^2=17 x^6+79 x^5+88 x^4+79 x^3+16 x^2+9 x+65$
• $y^2=21 x^6+60 x^5+55 x^4+72 x^3+76 x^2+49 x+31$
• $y^2=44 x^6+67 x^5+41 x^4+106 x^3+9 x^2+x+74$
• $y^2=43 x^6+65 x^5+102 x^4+95 x^3+53 x^2+65 x+72$
• $y^2=4 x^6+27 x^5+94 x^4+33 x^3+97 x^2+23$
• $y^2=76 x^6+60 x^5+26 x^4+90 x^3+79 x^2+35 x+110$
• $y^2=92 x^6+35 x^5+80 x^4+73 x^3+68 x^2+100 x+108$
• $y^2=73 x^6+34 x^5+77 x^4+51 x^3+89 x^2+105 x+88$
• $y^2=75 x^6+16 x^5+83 x^4+35 x^3+x^2+77 x+46$
• $y^2=68 x^6+81 x^5+65 x^4+29 x^3+48 x^2+92 x+69$
• and

• $y^2=57 x^6+48 x^5+93 x^4+101 x^3+83 x^2+43 x+29$
• $y^2=100 x^6+111 x^5+26 x^4+84 x^2+50 x+41$
• $y^2=69 x^6+20 x^5+94 x^4+52 x^3+61 x^2+78 x+2$
• $y^2=6 x^6+82 x^5+16 x^4+10 x^3+108 x^2+109 x+13$
• $y^2=28 x^6+92 x^4+100 x^3+78 x^2+76 x+105$
• $y^2=39 x^6+84 x^5+x^4+58 x^3+79 x^2+111 x+65$
• $y^2=79 x^6+43 x^5+x^4+14 x^3+27 x^2+72 x+3$
• $y^2=80 x^6+9 x^5+109 x^4+69 x^3+105 x^2+39 x+58$
• $y^2=110 x^6+80 x^5+4 x^4+46 x^3+97 x^2+110 x+25$
• $y^2=85 x^6+24 x^5+104 x^4+59 x^3+56 x^2+61 x+9$
• $y^2=20 x^6+33 x^5+24 x^4+13 x^3+37 x^2+93 x+106$
• $y^2=84 x^6+23 x^5+45 x^4+14 x^3+21 x^2+109 x+44$
• $y^2=112 x^6+6 x^5+30 x^4+38 x^3+35 x^2+x+72$
• $y^2=7 x^6+63 x^5+54 x^4+37 x^3+101 x^2+112 x$
• $y^2=71 x^6+77 x^5+48 x^4+8 x^3+36 x^2+38 x+39$
• $y^2=64 x^6+41 x^5+66 x^4+51 x^3+61 x^2+96 x+39$
• $y^2=38 x^6+43 x^5+93 x^4+50 x^3+79 x^2+59 x+40$
• $y^2=38 x^6+40 x^5+20 x^4+91 x^3+27 x^2+71 x+71$
• $y^2=95 x^6+22 x^5+43 x^4+25 x^3+65 x^2+30 x+52$
• $y^2=46 x^6+81 x^5+64 x^4+112 x^3+8 x^2+81 x+34$
• $y^2=17 x^6+64 x^5+33 x^4+32 x^2+28 x+27$
• $y^2=111 x^6+12 x^5+15 x^4+78 x^3+43 x^2+99 x+57$
• $y^2=91 x^6+60 x^5+31 x^4+22 x^3+88 x^2+10 x$
• $y^2=45 x^6+112 x^5+103 x^4+35 x^3+7 x^2+69 x+6$
• $y^2=65 x^6+98 x^5+44 x^4+44 x^3+9 x^2+21 x+55$
• $y^2=70 x^6+112 x^5+99 x^4+61 x^3+32 x^2+13 x+103$
• $y^2=78 x^6+57 x^5+96 x^4+59 x^3+58 x^2+56 x+93$
• $y^2=17 x^6+50 x^5+76 x^4+60 x^3+98 x^2+111 x+61$
• $y^2=91 x^6+11 x^5+44 x^4+109 x^2+94 x+65$
• $y^2=94 x^6+104 x^5+28 x^4+61 x^3+47 x^2+93 x+34$
• $y^2=60 x^6+37 x^5+75 x^4+27 x^3+41 x^2+21 x+33$
• $y^2=12 x^6+10 x^5+81 x^4+32 x^3+11 x^2+67 x+88$
• $y^2=80 x^6+88 x^5+108 x^4+2 x^3+50 x^2+36 x+103$
• $y^2=46 x^6+52 x^5+27 x^4+110 x^3+18 x^2+31 x+74$
• $y^2=101 x^6+61 x^5+77 x^4+11 x^3+23 x^2+x+64$
• $y^2=72 x^6+92 x^5+28 x^4+73 x^3+54 x^2+84$
• $y^2=72 x^6+69 x^5+101 x^4+34 x^3+36 x^2+64 x+45$
• $y^2=38 x^6+22 x^5+19 x^4+84 x^3+66 x^2+94 x+69$
• $y^2=105 x^6+19 x^5+104 x^4+6 x^3+23 x^2+30 x+109$
• $y^2=3 x^6+106 x^5+45 x^4+77 x^3+103 x^2+105 x+23$
• $y^2=4 x^6+60 x^5+6 x^4+33 x^3+101 x^2+109 x+26$
• $y^2=76 x^6+40 x^5+48 x^4+14 x^3+52 x^2+26 x+66$
• $y^2=68 x^6+26 x^5+101 x^4+55 x^3+70 x^2+58 x+37$
• $y^2=59 x^6+41 x^5+69 x^4+4 x^3+103 x^2+74 x+37$
• $y^2=17 x^6+97 x^5+30 x^4+96 x^3+40 x^2+106 x+23$
• $y^2=84 x^5+98 x^4+12 x^3+73 x^2+77 x+2$
• $y^2=8 x^6+108 x^5+95 x^4+81 x^3+107 x^2+92 x+5$
• $y^2=70 x^6+95 x^5+20 x^4+110 x^3+23 x^2+70 x+103$
• $y^2=96 x^6+106 x^5+41 x^4+41 x^3+103 x^2+70 x+66$
• $y^2=14 x^6+24 x^5+98 x^4+55 x^3+76 x^2+74 x+33$
• $y^2=3 x^6+107 x^5+69 x^4+94 x^3+12 x^2+72 x+41$
• $y^2=92 x^6+112 x^5+75 x^4+8 x^3+45 x^2+20 x+48$

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 4.0.1847600.2.

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.ba_pa	$2$	(not in LMFDB)