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

• Label: 2.113.aba_ov
• 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:	$1 - 26 x + 385 x^{2} - 2938 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.225096229457$, $\pm0.346870828388$
Angle rank:	$2$ (numerical)
Number field:	4.0.108430400.1
Galois group:	$D_{4}$
Jacobians:	$60$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10191$	$164268729$	$2087209782684$	$26589845533441401$	$339457998361520742591$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$12864$	$1446538$	$163080500$	$18424420148$	$2081950265718$	$235260533949620$	$26584441912727524$	$3004041937744861834$	$339456738969861846864$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 60 curves (of which all are hyperelliptic):

• $y^2=63 x^6+8 x^5+97 x^4+85 x^3+30 x^2+85 x+24$
• $y^2=47 x^6+100 x^5+46 x^4+8 x^3+96 x^2+9 x+100$
• $y^2=45 x^6+55 x^5+65 x^4+86 x^3+47 x^2+8 x+107$
• $y^2=42 x^6+5 x^5+42 x^4+55 x^3+49 x^2+15 x+102$
• $y^2=12 x^6+27 x^5+98 x^4+40 x^3+27 x^2+87 x+83$
• $y^2=93 x^6+94 x^5+33 x^4+42 x^3+98 x^2+70 x+79$
• $y^2=36 x^6+94 x^5+12 x^4+9 x^3+59 x^2+94$
• $y^2=105 x^6+71 x^5+14 x^4+35 x^3+5 x^2+76 x+74$
• $y^2=65 x^6+68 x^5+29 x^4+80 x^3+80 x^2+105 x+107$
• $y^2=95 x^6+7 x^5+3 x^4+11 x^3+57 x^2+23 x+105$
• $y^2=72 x^6+10 x^5+109 x^4+93 x^3+93 x^2+73 x+86$
• $y^2=18 x^6+86 x^5+47 x^4+84 x^3+40 x^2+13 x+88$
• $y^2=76 x^6+98 x^5+84 x^4+69 x^3+65 x^2+42 x+27$
• $y^2=38 x^6+88 x^5+87 x^4+22 x^3+36 x^2+106 x+37$
• $y^2=106 x^6+16 x^5+53 x^4+28 x^3+89 x^2+42 x+55$
• $y^2=59 x^6+14 x^5+92 x^4+26 x^3+47 x^2+102 x+67$
• $y^2=38 x^6+5 x^5+6 x^4+35 x^3+96 x^2+33 x+9$
• $y^2=8 x^6+3 x^5+88 x^4+51 x^3+81 x^2+88 x+84$
• $y^2=112 x^6+8 x^5+69 x^4+72 x^3+66 x^2+103 x+19$
• $y^2=15 x^6+96 x^5+86 x^4+111 x^3+48 x^2+91 x+95$
• and

• $y^2=102 x^6+52 x^5+69 x^4+39 x^3+36 x^2+35 x+38$
• $y^2=99 x^6+2 x^5+85 x^4+28 x^3+x+26$
• $y^2=71 x^6+68 x^5+63 x^4+52 x^3+9 x^2+30 x+42$
• $y^2=74 x^6+92 x^5+62 x^4+8 x^3+55 x^2+18 x+43$
• $y^2=100 x^6+87 x^5+29 x^4+82 x^3+25 x^2+4 x+32$
• $y^2=64 x^6+8 x^5+94 x^4+5 x^3+37 x^2+112 x+105$
• $y^2=81 x^6+56 x^5+18 x^4+63 x^3+15 x^2+20 x+91$
• $y^2=17 x^6+4 x^5+99 x^4+36 x^3+33 x^2+83 x+27$
• $y^2=3 x^6+91 x^5+14 x^4+65 x^3+58 x^2+76 x+27$
• $y^2=54 x^6+14 x^5+38 x^4+61 x^3+69 x^2+95 x+74$
• $y^2=86 x^6+5 x^5+43 x^4+89 x^3+23 x^2+29 x+44$
• $y^2=19 x^6+48 x^5+2 x^4+46 x^2+33 x+109$
• $y^2=46 x^6+39 x^5+72 x^4+14 x^3+32 x^2+105 x+48$
• $y^2=110 x^6+49 x^5+106 x^4+51 x^3+38 x^2+106 x+90$
• $y^2=9 x^6+44 x^5+48 x^4+41 x^3+97 x^2+74 x+106$
• $y^2=78 x^6+105 x^5+106 x^4+40 x^3+66 x^2+26 x+15$
• $y^2=96 x^6+110 x^5+42 x^4+55 x^3+77 x^2+78 x+10$
• $y^2=75 x^6+19 x^5+30 x^4+54 x^3+111 x^2+3 x+34$
• $y^2=100 x^6+74 x^5+104 x^4+63 x^3+79 x^2+98 x+57$
• $y^2=32 x^6+2 x^5+25 x^4+54 x^3+96 x^2+25 x+57$
• $y^2=75 x^6+4 x^5+106 x^4+58 x^3+85 x^2+x+4$
• $y^2=74 x^6+20 x^5+77 x^4+25 x^3+31 x^2+60 x+21$
• $y^2=60 x^6+97 x^5+8 x^4+106 x^3+97 x^2+82 x+28$
• $y^2=86 x^6+68 x^5+16 x^4+62 x^3+33 x^2+25 x+17$
• $y^2=103 x^6+81 x^4+24 x^3+70 x^2+94 x+95$
• $y^2=13 x^6+44 x^5+35 x^4+112 x^3+74 x^2+35 x+90$
• $y^2=67 x^6+83 x^5+31 x^4+43 x^3+45 x^2+51 x+14$
• $y^2=46 x^6+53 x^5+51 x^4+5 x^3+50 x^2+69 x+15$
• $y^2=10 x^6+109 x^5+35 x^4+5 x^3+66 x^2+12 x+48$
• $y^2=75 x^6+4 x^5+43 x^4+45 x^3+63 x^2+102 x+89$
• $y^2=109 x^6+6 x^5+100 x^4+2 x^3+61 x^2+24 x+74$
• $y^2=7 x^6+67 x^5+61 x^4+39 x^3+48 x^2+9 x+39$
• $y^2=16 x^6+45 x^5+71 x^4+109 x^3+56 x^2+104 x+110$
• $y^2=71 x^6+38 x^5+71 x^4+59 x^3+41 x^2+45 x+99$
• $y^2=37 x^6+99 x^5+40 x^4+99 x^3+111 x^2+37 x+71$
• $y^2=28 x^6+91 x^5+76 x^4+67 x^3+35 x^2+108 x+43$
• $y^2=51 x^6+109 x^5+58 x^4+21 x^2+110 x+84$
• $y^2=78 x^6+39 x^5+37 x^4+111 x^3+8 x^2+55 x+14$
• $y^2=83 x^6+110 x^5+73 x^4+57 x^3+69 x^2+73 x+67$
• $y^2=57 x^6+64 x^5+103 x^4+96 x^3+33 x^2+95 x+56$

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 4.0.108430400.1.

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.ba_ov	$2$	(not in LMFDB)