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

• Label: 2.113.az_od
• 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:	$1 - 25 x + 367 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.219440650796$, $\pm0.367525988332$
Angle rank:	$2$ (numerical)
Number field:	4.0.257303429.1
Galois group:	$D_{4}$
Jacobians:	$65$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10287$	$164458269$	$2086899176079$	$26588693445738021$	$339457144303470658032$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12879$	$1446323$	$163073435$	$18424373794$	$2081951017623$	$235260551518543$	$26584442014871539$	$3004041936497335349$	$339456738942756065214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 65 curves (of which all are hyperelliptic):

• $y^2=48 x^6+101 x^5+74 x^4+54 x^3+102 x^2+59 x+10$
• $y^2=31 x^6+83 x^5+74 x^4+94 x^3+88 x^2+103 x+101$
• $y^2=24 x^6+58 x^5+81 x^4+106 x^3+19 x^2+39 x+47$
• $y^2=22 x^6+38 x^5+4 x^4+38 x^3+94 x^2+23 x+82$
• $y^2=82 x^6+84 x^5+24 x^4+81 x^3+36 x^2+38 x+90$
• $y^2=21 x^6+81 x^5+107 x^4+24 x^3+111 x^2+42 x+28$
• $y^2=103 x^6+78 x^5+108 x^4+101 x^3+6 x^2+31 x+40$
• $y^2=50 x^6+90 x^5+34 x^4+101 x^3+54 x^2+60 x+93$
• $y^2=47 x^6+21 x^5+31 x^3+x^2+99 x+6$
• $y^2=110 x^6+69 x^5+57 x^4+75 x^3+32 x^2+3 x+61$
• $y^2=72 x^6+5 x^5+56 x^4+31 x^3+81 x^2+31 x+67$
• $y^2=35 x^6+85 x^5+95 x^4+98 x^3+58 x^2+7 x+54$
• $y^2=68 x^6+33 x^5+99 x^4+64 x^3+77 x^2+102 x+83$
• $y^2=99 x^6+66 x^5+9 x^4+51 x^3+25 x^2+105 x+21$
• $y^2=85 x^6+29 x^5+108 x^4+10 x^3+82 x^2+7 x+73$
• $y^2=65 x^6+31 x^5+87 x^4+16 x^3+62 x^2+60 x+29$
• $y^2=25 x^6+72 x^5+31 x^4+79 x^3+56 x^2+105 x+30$
• $y^2=51 x^6+88 x^5+82 x^4+109 x^3+105 x^2+5 x+81$
• $y^2=47 x^6+106 x^5+84 x^4+90 x^3+90 x^2+67 x+6$
• $y^2=81 x^6+97 x^5+6 x^4+27 x^3+56 x^2+43 x+50$
• and

• $y^2=72 x^6+29 x^5+9 x^4+111 x^3+35 x^2+47 x+63$
• $y^2=99 x^6+97 x^5+68 x^4+18 x^3+97 x^2+11$
• $y^2=10 x^6+32 x^5+38 x^4+99 x^3+59 x^2+100 x+103$
• $y^2=63 x^6+16 x^5+96 x^4+84 x^3+95 x^2+89 x+103$
• $y^2=3 x^6+67 x^5+101 x^4+3 x^3+2 x^2+70 x+26$
• $y^2=3 x^6+19 x^5+34 x^4+24 x^3+49 x^2+39 x+38$
• $y^2=28 x^6+14 x^5+11 x^4+99 x^3+90 x^2+60 x+59$
• $y^2=11 x^6+58 x^5+56 x^4+54 x^3+33 x^2+104 x+76$
• $y^2=51 x^6+82 x^5+48 x^4+71 x^3+112 x^2+78 x+53$
• $y^2=15 x^6+55 x^5+77 x^4+38 x^3+91 x^2+102 x+110$
• $y^2=7 x^6+63 x^5+60 x^4+16 x^3+67 x^2+49 x+42$
• $y^2=31 x^6+68 x^5+89 x^4+6 x^3+55 x^2+26 x+20$
• $y^2=97 x^6+46 x^5+112 x^4+65 x^3+63 x^2+14 x+65$
• $y^2=30 x^6+72 x^5+56 x^4+14 x^3+49 x^2+59 x+49$
• $y^2=43 x^6+7 x^5+10 x^4+94 x^3+42 x^2+104 x+54$
• $y^2=40 x^6+98 x^5+81 x^4+112 x^3+109 x^2+106 x+98$
• $y^2=86 x^6+17 x^5+72 x^4+96 x^3+4 x^2+20 x+79$
• $y^2=41 x^6+23 x^5+84 x^4+77 x^3+60 x^2+50 x+32$
• $y^2=65 x^6+29 x^5+54 x^4+25 x^3+112 x^2+17 x+103$
• $y^2=111 x^6+80 x^5+34 x^4+42 x^2+53 x+61$
• $y^2=86 x^6+57 x^5+66 x^4+37 x^3+80 x^2+108 x+23$
• $y^2=27 x^6+28 x^5+85 x^4+74 x^3+8 x^2+100 x+106$
• $y^2=14 x^6+28 x^5+110 x^4+108 x^3+43 x^2+80 x+30$
• $y^2=71 x^6+69 x^5+97 x^4+3 x^3+108 x^2+105 x+9$
• $y^2=59 x^6+40 x^5+40 x^4+51 x^3+40 x^2+69 x+101$
• $y^2=34 x^6+65 x^5+65 x^4+27 x^3+13 x^2+48 x+58$
• $y^2=80 x^6+99 x^5+88 x^4+106 x^3+39 x^2+10 x+34$
• $y^2=33 x^6+61 x^5+94 x^4+28 x^3+40 x^2+110 x+38$
• $y^2=54 x^6+14 x^5+5 x^4+25 x^3+79 x^2+4 x+41$
• $y^2=19 x^6+23 x^5+104 x^4+37 x^3+107 x^2+43 x+12$
• $y^2=6 x^6+81 x^5+27 x^4+17 x^3+83 x^2+98 x+33$
• $y^2=109 x^6+56 x^5+35 x^4+73 x^3+5 x^2+80 x+29$
• $y^2=40 x^6+87 x^5+16 x^4+105 x^3+42 x^2+52 x+92$
• $y^2=22 x^6+84 x^5+44 x^4+51 x^3+49 x^2+66 x+59$
• $y^2=40 x^6+77 x^5+103 x^4+81 x^3+58 x^2+65 x+51$
• $y^2=112 x^6+6 x^5+106 x^4+71 x^3+33 x^2+38 x+37$
• $y^2=31 x^6+27 x^5+14 x^4+55 x^3+83 x^2+21 x+37$
• $y^2=108 x^6+27 x^5+69 x^4+94 x^3+112 x^2+87 x+20$
• $y^2=97 x^6+23 x^5+111 x^4+47 x^3+31 x^2+72 x+46$
• $y^2=40 x^6+3 x^5+58 x^4+60 x^3+106 x^2+61 x+76$
• $y^2=3 x^6+94 x^5+39 x^4+99 x^3+67 x^2+24 x+101$
• $y^2=92 x^6+41 x^5+70 x^4+48 x^3+90 x^2+27 x+15$
• $y^2=55 x^6+84 x^5+30 x^4+38 x^3+52 x^2+73 x+78$
• $y^2=79 x^6+85 x^5+2 x^4+110 x^3+25 x^2+112 x+58$
• $y^2=31 x^6+90 x^5+26 x^4+29 x^3+86 x^2+51 x+53$

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 4.0.257303429.1.

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_od	$2$	(not in LMFDB)