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

• Label: 2.113.az_mr
• 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:	$1 - 25 x + 329 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.118776341890$, $\pm0.421305169432$
Angle rank:	$2$ (numerical)
Number field:	4.0.1158043725.1
Galois group:	$D_{4}$
Jacobians:	$72$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10249$	$163461301$	$2082782604121$	$26581828470903781$	$339453468686393653264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12803$	$1443473$	$163031331$	$18424174294$	$2081953792307$	$235260604804993$	$26584442380270723$	$3004041938618972249$	$339456738993945611678$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

• $y^2=4 x^6+25 x^5+49 x^4+2 x^3+22 x^2+46 x+78$
• $y^2=95 x^6+54 x^5+109 x^4+28 x^3+110 x^2+74 x+92$
• $y^2=92 x^6+58 x^5+6 x^4+51 x^3+82 x^2+28 x+88$
• $y^2=32 x^6+11 x^5+33 x^4+95 x^3+107 x^2+79 x+85$
• $y^2=34 x^6+34 x^5+82 x^4+54 x^3+65 x^2+94 x+65$
• $y^2=68 x^6+73 x^5+67 x^4+39 x^3+59 x^2+41$
• $y^2=33 x^6+54 x^5+28 x^4+55 x^3+80 x^2+52 x+23$
• $y^2=11 x^6+22 x^5+81 x^4+94 x^3+51 x^2+94 x$
• $y^2=37 x^6+67 x^5+109 x^4+15 x^3+90 x^2+86 x+11$
• $y^2=80 x^6+12 x^5+104 x^4+87 x^3+4 x^2+33 x+67$
• $y^2=91 x^6+75 x^5+96 x^4+15 x^3+12 x^2+65 x+28$
• $y^2=108 x^6+35 x^5+30 x^4+76 x^3+25 x^2+72 x+63$
• $y^2=85 x^6+2 x^5+24 x^4+40 x^3+53 x^2+62 x+7$
• $y^2=20 x^6+31 x^5+54 x^4+6 x^3+51 x^2+88 x+72$
• $y^2=21 x^6+87 x^5+10 x^4+53 x^3+101 x^2+12 x+93$
• $y^2=80 x^6+49 x^5+27 x^4+48 x^3+13 x^2+18 x+55$
• $y^2=33 x^6+25 x^5+106 x^4+44 x^3+6 x^2+53 x+48$
• $y^2=61 x^5+95 x^4+91 x^3+25 x^2+34 x+63$
• $y^2=65 x^6+47 x^5+85 x^4+61 x^2+89 x+70$
• $y^2=88 x^6+15 x^5+60 x^4+31 x^3+23 x^2+70 x+13$
• and

• $y^2=17 x^6+56 x^5+107 x^4+85 x^3+109 x^2+48 x+27$
• $y^2=16 x^6+97 x^5+33 x^4+56 x^3+33 x^2+81 x+90$
• $y^2=38 x^6+107 x^5+11 x^4+107 x^3+15 x^2+74 x+72$
• $y^2=38 x^6+111 x^5+99 x^4+30 x^3+76 x^2+37 x+2$
• $y^2=111 x^6+65 x^5+92 x^4+39 x^3+98 x^2+12 x+54$
• $y^2=20 x^6+94 x^5+48 x^4+41 x^3+67 x^2+7 x+101$
• $y^2=67 x^6+88 x^5+29 x^4+32 x^3+88 x^2+104 x+88$
• $y^2=24 x^6+16 x^5+58 x^4+17 x^3+108 x^2+21 x+16$
• $y^2=59 x^6+82 x^5+7 x^4+15 x^3+11 x^2+101 x+80$
• $y^2=84 x^6+101 x^5+79 x^4+7 x^3+78 x^2+110 x+94$
• $y^2=21 x^6+22 x^5+102 x^4+48 x^3+46 x^2+72 x+89$
• $y^2=20 x^6+56 x^5+83 x^4+99 x^3+37 x^2+101 x+61$
• $y^2=47 x^6+22 x^5+21 x^4+57 x^2+89 x+58$
• $y^2=24 x^6+102 x^5+91 x^4+93 x^3+32 x^2+97 x+38$
• $y^2=59 x^6+7 x^5+74 x^4+90 x^3+45 x^2+109 x+87$
• $y^2=35 x^6+99 x^5+72 x^4+56 x^3+32 x^2+66 x+63$
• $y^2=59 x^6+90 x^5+95 x^4+35 x^3+72 x^2+53 x+78$
• $y^2=38 x^6+80 x^5+63 x^4+57 x^3+6 x^2+61 x+112$
• $y^2=108 x^5+2 x^4+42 x^3+65 x^2+24 x+100$
• $y^2=83 x^6+10 x^5+6 x^4+18 x^3+108 x^2+x+99$
• $y^2=21 x^6+110 x^5+6 x^4+88 x^3+83 x^2+37 x+98$
• $y^2=22 x^6+46 x^5+66 x^4+51 x^3+49 x^2+73 x+21$
• $y^2=39 x^6+3 x^5+102 x^4+89 x^3+13 x^2+51 x+50$
• $y^2=70 x^6+52 x^5+103 x^4+81 x^3+66 x^2+53 x+99$
• $y^2=42 x^6+16 x^5+67 x^4+88 x^3+106 x^2+27 x+48$
• $y^2=44 x^6+77 x^5+25 x^4+60 x^3+66 x^2+13 x+50$
• $y^2=92 x^6+2 x^5+5 x^4+21 x^3+16 x^2+75 x+77$
• $y^2=105 x^6+107 x^5+53 x^4+67 x^3+47 x^2+43 x+61$
• $y^2=66 x^6+77 x^5+72 x^4+39 x^3+53 x^2+42 x$
• $y^2=99 x^6+63 x^5+18 x^4+99 x^3+70 x+75$
• $y^2=20 x^6+69 x^5+x^4+107 x^3+59 x^2+27 x+6$
• $y^2=47 x^6+95 x^5+99 x^4+26 x^3+35 x^2+5 x+18$
• $y^2=37 x^6+76 x^5+30 x^4+26 x^3+46 x^2+37 x+69$
• $y^2=16 x^6+90 x^5+7 x^4+9 x^3+76 x^2+59 x+38$
• $y^2=12 x^6+46 x^5+24 x^4+65 x^3+85 x^2+27 x+90$
• $y^2=4 x^6+88 x^5+45 x^3+88 x^2+24 x+41$
• $y^2=45 x^6+48 x^5+x^4+3 x^3+49 x^2+16 x+14$
• $y^2=20 x^6+5 x^5+78 x^4+15 x^3+39 x^2+8 x+31$
• $y^2=80 x^6+36 x^5+76 x^4+52 x^3+33 x^2+27 x+23$
• $y^2=11 x^6+19 x^5+48 x^4+99 x^3+107 x^2+48 x+3$
• $y^2=39 x^6+52 x^5+65 x^4+52 x^3+25 x^2+45 x+91$
• $y^2=45 x^6+74 x^5+25 x^4+96 x^3+102 x^2+19 x+6$
• $y^2=3 x^6+53 x^5+100 x^4+64 x^3+66 x^2+65 x+17$
• $y^2=15 x^6+62 x^5+65 x^4+6 x^3+49 x^2+69 x+103$
• $y^2=91 x^6+68 x^5+34 x^4+35 x^3+55 x^2+80 x+28$
• $y^2=62 x^6+x^5+5 x^4+19 x^3+30 x^2+81 x+96$
• $y^2=53 x^6+42 x^5+64 x^4+65 x^3+104 x^2+79 x+101$
• $y^2=38 x^6+48 x^5+85 x^4+26 x^3+26 x^2+67 x+35$
• $y^2=14 x^6+14 x^5+68 x^4+112 x^3+63 x^2+47 x+12$
• $y^2=74 x^6+67 x^5+86 x^4+2 x^3+51 x^2+26 x+107$
• $y^2=110 x^6+35 x^5+46 x^4+74 x^3+15 x^2+7$
• $y^2=59 x^6+63 x^5+100 x^4+83 x^3+61 x^2+72 x+73$

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 4.0.1158043725.1.

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_mr	$2$	(not in LMFDB)