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

• Label: 2.113.az_oi
• 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:	$1 - 25 x + 372 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.235515891975$, $\pm0.355912945687$
Angle rank:	$2$ (numerical)
Number field:	4.0.31562456.1
Galois group:	$D_{4}$
Jacobians:	$54$
Isomorphism classes:	54

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10292$	$164589664$	$2087441059904$	$26589526713424256$	$339457132801470154132$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12889$	$1446698$	$163078545$	$18424373169$	$2081949902398$	$235260533407793$	$26584441913626209$	$3004041937543502474$	$339456738969221909289$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 54 curves (of which all are hyperelliptic):

• $y^2=38 x^6+35 x^5+30 x^4+52 x^3+34 x^2+13 x+102$
• $y^2=83 x^6+20 x^5+39 x^4+35 x^3+26 x^2+29 x+31$
• $y^2=39 x^6+76 x^5+109 x^4+47 x^3+63 x^2+57 x+27$
• $y^2=78 x^6+27 x^5+88 x^3+98 x^2+84 x+11$
• $y^2=101 x^6+61 x^5+60 x^4+105 x^3+67 x^2+61 x+105$
• $y^2=38 x^6+74 x^5+x^4+69 x^3+57 x^2+68 x+25$
• $y^2=69 x^6+78 x^5+27 x^4+73 x^3+53 x^2+49 x+55$
• $y^2=6 x^6+4 x^5+32 x^4+64 x^3+59 x^2+41 x+27$
• $y^2=27 x^6+45 x^5+91 x^4+92 x^3+7 x^2+23 x+21$
• $y^2=24 x^6+107 x^5+80 x^4+42 x^3+96 x^2+65 x+33$
• $y^2=82 x^6+18 x^5+96 x^4+88 x^3+45 x^2+69 x+12$
• $y^2=37 x^6+34 x^5+112 x^4+57 x^3+105 x^2+x+90$
• $y^2=23 x^6+46 x^5+41 x^4+53 x^3+85 x^2+79 x+70$
• $y^2=34 x^6+43 x^5+43 x^4+33 x^3+17 x^2+92 x+2$
• $y^2=63 x^6+36 x^5+105 x^4+83 x^3+60 x^2+74 x+60$
• $y^2=75 x^6+22 x^5+112 x^4+53 x^3+40 x^2+32 x+31$
• $y^2=19 x^6+3 x^5+95 x^4+88 x^3+93 x^2+25 x+69$
• $y^2=67 x^6+28 x^5+81 x^4+34 x^3+109 x^2+96 x+54$
• $y^2=19 x^6+85 x^5+111 x^4+98 x^3+33 x^2+81 x+10$
• $y^2=32 x^6+109 x^5+10 x^4+97 x^3+72 x^2+49 x+111$
• and

• $y^2=6 x^6+74 x^5+89 x^4+18 x^3+19 x^2+x+20$
• $y^2=86 x^6+74 x^5+46 x^4+111 x^3+66 x^2+44 x+9$
• $y^2=23 x^6+102 x^5+78 x^4+81 x^3+100 x^2+25 x+63$
• $y^2=75 x^6+102 x^5+87 x^4+21 x^3+90 x^2+45 x+99$
• $y^2=75 x^6+112 x^5+74 x^4+11 x^3+43 x^2+82 x+108$
• $y^2=3 x^6+39 x^5+34 x^4+33 x^3+74 x^2+51 x+38$
• $y^2=33 x^6+49 x^5+63 x^4+36 x^3+82 x^2+70 x+39$
• $y^2=48 x^6+29 x^5+11 x^4+6 x^3+49 x^2+62 x+96$
• $y^2=7 x^6+88 x^5+36 x^4+100 x^3+33 x^2+20 x+67$
• $y^2=76 x^6+79 x^5+26 x^4+11 x^3+69 x^2+39 x+46$
• $y^2=2 x^6+71 x^5+85 x^4+17 x^3+17 x^2+58 x+66$
• $y^2=7 x^6+10 x^5+89 x^4+28 x^3+107 x^2+107 x+58$
• $y^2=46 x^6+89 x^5+84 x^4+6 x^3+18 x^2+81 x+1$
• $y^2=42 x^6+82 x^5+9 x^4+20 x^3+47 x^2+86 x+101$
• $y^2=94 x^6+16 x^5+33 x^4+104 x^3+42 x^2+28 x+78$
• $y^2=75 x^6+28 x^5+45 x^4+77 x^3+24 x^2+99 x+25$
• $y^2=x^6+73 x^5+9 x^4+57 x^3+46 x^2+24 x+33$
• $y^2=65 x^6+56 x^5+76 x^4+50 x^3+60 x^2+49 x+102$
• $y^2=112 x^6+36 x^5+83 x^4+11 x^3+105 x^2+38 x+78$
• $y^2=28 x^6+100 x^5+32 x^4+25 x^3+91 x^2+78 x+98$
• $y^2=67 x^6+52 x^5+58 x^4+29 x^3+23 x^2+16 x+78$
• $y^2=19 x^6+103 x^5+83 x^4+106 x^3+105 x^2+29 x+71$
• $y^2=97 x^6+104 x^5+8 x^4+56 x^3+50 x^2+31 x+79$
• $y^2=46 x^6+44 x^5+83 x^4+34 x^3+48 x^2+68 x+82$
• $y^2=64 x^6+111 x^5+4 x^4+67 x^3+76 x^2+52 x+36$
• $y^2=98 x^6+18 x^5+26 x^4+73 x^3+105 x^2+76 x+106$
• $y^2=31 x^6+65 x^5+56 x^4+56 x^3+35 x^2+33 x+80$
• $y^2=53 x^6+49 x^5+15 x^4+3 x^3+10 x^2+105 x+29$
• $y^2=66 x^6+39 x^5+54 x^4+46 x^3+37 x^2+83 x+82$
• $y^2=25 x^6+52 x^5+64 x^4+32 x^3+53 x^2+96 x+36$
• $y^2=63 x^6+16 x^5+65 x^4+72 x^3+84 x^2+43 x+72$
• $y^2=95 x^6+21 x^5+73 x^4+108 x^3+85 x^2+83 x+100$
• $y^2=24 x^6+36 x^5+22 x^4+66 x^3+97 x^2+110 x+24$
• $y^2=85 x^6+64 x^5+72 x^4+79 x^3+20 x^2+37 x+83$

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 4.0.31562456.1.

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.z_oi	$2$	(not in LMFDB)