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

• Label: 2.113.az_mc
• 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:	$1 - 25 x + 314 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0690964705090$, $\pm0.436110748201$
Angle rank:	$2$ (numerical)
Number field:	4.0.678213900.1
Galois group:	$D_{4}$
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10234$	$163068556$	$2081158444456$	$26578859643164416$	$339450186897965643514$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12773$	$1442348$	$163013121$	$18423996169$	$2081952021602$	$235260576727993$	$26584441994262913$	$3004041935908594124$	$339456738997453314053$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which all are hyperelliptic):

• $y^2=98 x^6+92 x^5+93 x^4+110 x^3+33 x^2+88 x+69$
• $y^2=108 x^6+42 x^5+81 x^4+x^3+67 x^2+90 x+78$
• $y^2=90 x^6+66 x^5+53 x^4+84 x^3+103 x^2+21 x+25$
• $y^2=12 x^6+74 x^5+46 x^4+101 x^3+49 x^2+35 x+91$
• $y^2=26 x^6+70 x^5+102 x^4+76 x^3+67 x^2+67 x+12$
• $y^2=110 x^6+33 x^5+40 x^4+106 x^3+21 x^2+83 x+6$
• $y^2=80 x^6+38 x^5+3 x^4+91 x^3+111 x^2+96 x+15$
• $y^2=97 x^6+60 x^5+87 x^4+15 x^3+100 x^2+33 x+108$
• $y^2=19 x^6+93 x^5+46 x^4+73 x^3+54 x^2+x+27$
• $y^2=75 x^6+53 x^5+65 x^4+59 x^3+30 x^2+33 x+107$
• $y^2=6 x^6+58 x^5+98 x^4+33 x^3+26 x^2+78 x+51$
• $y^2=54 x^6+69 x^5+21 x^4+15 x^3+88 x^2+28 x+69$
• $y^2=6 x^6+26 x^5+45 x^4+81 x^3+76 x^2+73 x+93$
• $y^2=55 x^6+8 x^5+30 x^4+66 x^3+74 x^2+67 x+71$
• $y^2=54 x^6+6 x^5+63 x^4+88 x^3+6 x^2+83 x+42$
• $y^2=4 x^6+41 x^5+111 x^4+13 x^3+10 x^2+110 x+4$
• $y^2=15 x^6+93 x^5+20 x^4+93 x^3+56 x^2+x+90$
• $y^2=21 x^6+74 x^5+75 x^4+13 x^3+57 x^2+25 x+38$
• $y^2=66 x^6+57 x^5+43 x^4+76 x^3+50 x^2+85 x+21$
• $y^2=85 x^6+56 x^5+75 x^4+27 x^3+85 x^2+55 x+45$
• and

• $y^2=45 x^6+14 x^5+47 x^4+43 x^3+58 x^2+27 x+38$
• $y^2=109 x^6+88 x^5+67 x^4+22 x^3+94 x^2+45 x+92$
• $y^2=19 x^6+94 x^5+105 x^4+92 x^3+55 x^2+94 x+71$
• $y^2=37 x^6+38 x^5+48 x^4+106 x^3+99 x^2+3 x+84$
• $y^2=107 x^6+9 x^5+50 x^4+32 x^3+22 x^2+62 x+67$
• $y^2=51 x^6+70 x^5+14 x^4+108 x^3+87 x^2+40 x+27$
• $y^2=14 x^6+49 x^5+93 x^4+63 x^3+73 x^2+45 x+90$
• $y^2=67 x^6+87 x^5+29 x^4+48 x^3+108 x^2+26 x+90$
• $y^2=52 x^6+32 x^5+16 x^4+45 x^3+39 x^2+81 x+39$
• $y^2=32 x^6+2 x^5+90 x^4+3 x^3+92 x^2+14 x+96$
• $y^2=70 x^5+64 x^4+29 x^3+72 x^2+70 x+60$
• $y^2=72 x^6+38 x^5+9 x^4+95 x^3+23 x^2+68 x+5$

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 4.0.678213900.1.

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_mc	$2$	(not in LMFDB)