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

• Label: 2.113.az_mp
• 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:	$1 - 25 x + 327 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.113069054797$, $\pm0.423400014177$
Angle rank:	$2$ (numerical)
Number field:	4.0.1138434869.1
Galois group:	$D_{4}$
Jacobians:	$56$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10247$	$163408909$	$2082566024279$	$26581441098030341$	$339453090993396117232$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12799$	$1443323$	$163028955$	$18424153794$	$2081953652023$	$235260602849543$	$26584442353763379$	$3004041938574703349$	$339456738998676343614$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=29 x^6+39 x^5+16 x^4+97 x^3+82 x^2+42 x+50$
• $y^2=25 x^6+106 x^5+110 x^4+41 x^3+14 x^2+98 x+79$
• $y^2=105 x^6+42 x^5+6 x^4+83 x^3+15 x^2+22 x+63$
• $y^2=10 x^6+67 x^5+6 x^4+44 x^3+72 x^2+26 x+36$
• $y^2=77 x^5+34 x^4+111 x^3+30 x^2+90 x+23$
• $y^2=80 x^6+77 x^5+x^4+82 x^3+12 x^2+59 x+108$
• $y^2=47 x^6+104 x^5+10 x^4+39 x^3+80 x^2+77 x+34$
• $y^2=65 x^6+45 x^5+89 x^4+56 x^3+89 x^2+x+62$
• $y^2=64 x^6+74 x^5+23 x^4+41 x^3+70 x^2+91 x+53$
• $y^2=12 x^6+47 x^5+72 x^4+15 x^3+85 x^2+98 x+78$
• $y^2=41 x^6+90 x^5+60 x^4+24 x^3+13 x^2+93 x+76$
• $y^2=62 x^6+100 x^5+70 x^4+45 x^3+41 x^2+3 x+19$
• $y^2=45 x^6+42 x^5+62 x^4+85 x^3+16 x^2+109 x+27$
• $y^2=51 x^6+66 x^5+90 x^4+12 x^3+70 x^2+109 x+94$
• $y^2=7 x^6+12 x^5+37 x^4+35 x^3+76 x^2+6 x+72$
• $y^2=82 x^6+30 x^5+41 x^4+3 x^3+3 x^2+44 x+47$
• $y^2=45 x^6+38 x^5+97 x^4+59 x^3+101 x^2+45 x+28$
• $y^2=21 x^6+98 x^5+28 x^4+45 x^3+91 x^2+105 x+43$
• $y^2=29 x^6+92 x^5+94 x^4+92 x^3+35 x^2+36 x+67$
• $y^2=4 x^6+92 x^5+26 x^4+26 x^3+3 x^2+62 x+80$
• and

• $y^2=76 x^6+75 x^5+107 x^4+50 x^3+55 x^2+63 x+42$
• $y^2=95 x^6+83 x^5+43 x^4+60 x^3+46 x^2+47 x+30$
• $y^2=22 x^6+22 x^5+76 x^4+63 x^3+3 x^2+78 x+2$
• $y^2=19 x^6+14 x^5+89 x^4+64 x^3+47 x^2+30 x+39$
• $y^2=65 x^6+74 x^5+83 x^4+51 x^3+57 x^2+102 x+85$
• $y^2=46 x^6+105 x^5+107 x^4+26 x^3+89 x^2+27 x+46$
• $y^2=83 x^6+16 x^5+67 x^4+41 x^3+17 x^2+110 x+55$
• $y^2=106 x^6+2 x^5+106 x^4+103 x^3+14 x^2+10 x+91$
• $y^2=49 x^6+33 x^5+4 x^4+34 x^3+52 x^2+51 x+26$
• $y^2=61 x^6+75 x^5+89 x^4+99 x^3+102 x^2+19 x$
• $y^2=9 x^6+65 x^5+84 x^4+29 x^3+95 x^2+8 x+86$
• $y^2=110 x^6+22 x^5+82 x^4+42 x^3+7 x^2+101 x+65$
• $y^2=89 x^6+8 x^5+52 x^4+6 x^3+53 x^2+81 x+51$
• $y^2=23 x^6+60 x^5+29 x^4+97 x^3+4 x^2+37 x+78$
• $y^2=22 x^6+65 x^5+11 x^4+20 x^3+46 x^2+23 x+94$
• $y^2=50 x^6+27 x^5+68 x^4+97 x^3+66 x^2+5 x+79$
• $y^2=66 x^6+48 x^5+18 x^4+85 x^3+49 x^2+69 x+92$
• $y^2=52 x^6+62 x^5+71 x^4+97 x^3+61 x^2+79 x+79$
• $y^2=79 x^6+112 x^4+67 x^3+63 x^2+83 x+89$
• $y^2=2 x^6+87 x^5+102 x^4+48 x^3+47 x^2+25 x+69$
• $y^2=50 x^6+88 x^5+32 x^4+105 x^3+29 x^2+91 x+83$
• $y^2=7 x^6+75 x^5+99 x^4+96 x^3+24 x^2+51 x+93$
• $y^2=70 x^6+19 x^5+16 x^4+72 x^3+60 x^2+80 x+83$
• $y^2=53 x^6+5 x^5+48 x^4+15 x^3+12 x^2+84 x+44$
• $y^2=38 x^6+77 x^5+84 x^4+47 x^3+24 x^2+52 x+56$
• $y^2=17 x^6+67 x^5+40 x^4+109 x^3+2 x^2+12 x+78$
• $y^2=60 x^6+2 x^5+109 x^4+16 x^3+58 x^2+89 x+107$
• $y^2=23 x^6+95 x^5+69 x^4+78 x^3+71 x^2+25 x+15$
• $y^2=74 x^6+44 x^5+33 x^4+74 x^3+100 x^2+58 x+95$
• $y^2=15 x^6+48 x^5+26 x^4+112 x^3+64 x^2+32 x+71$
• $y^2=89 x^6+97 x^5+33 x^4+59 x^3+44 x^2+x+100$
• $y^2=90 x^6+13 x^5+75 x^4+50 x^3+74 x^2+65 x+95$
• $y^2=83 x^6+36 x^5+55 x^4+69 x^3+84 x^2+5 x+42$
• $y^2=78 x^6+15 x^5+43 x^4+94 x^3+12 x^2+59 x+105$
• $y^2=87 x^6+73 x^5+10 x^4+69 x^3+15 x^2+101 x+73$
• $y^2=95 x^6+107 x^5+47 x^4+52 x^3+34 x^2+40 x+93$

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 4.0.1138434869.1.

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_mp	$2$	(not in LMFDB)