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

• Label: 2.113.az_lv
• 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:	$1 - 25 x + 307 x^{2} - 2825 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0285761308447$, $\pm0.442413484536$
Angle rank:	$2$ (numerical)
Number field:	4.0.143964989.1
Galois group:	$D_{4}$
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10227$	$162885429$	$2080400649579$	$26577424012937301$	$339448300728147638832$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$12759$	$1441823$	$163004315$	$18423893794$	$2081950621623$	$235260552495043$	$26584441643350099$	$3004041932128357349$	$339456738960552266814$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):

• $y^2=34 x^6+45 x^5+16 x^4+61 x^3+12 x^2+75 x+51$
• $y^2=11 x^6+16 x^5+105 x^4+46 x^3+102 x^2+23 x+110$
• $y^2=45 x^6+60 x^5+26 x^4+38 x^3+104 x^2+34 x+17$
• $y^2=108 x^6+112 x^5+37 x^4+81 x^3+22 x^2+32 x+16$
• $y^2=41 x^6+60 x^5+110 x^4+101 x^3+111 x^2+81 x+102$
• $y^2=87 x^6+74 x^5+69 x^4+77 x^3+43 x^2+13 x+88$
• $y^2=55 x^6+73 x^5+89 x^4+94 x^3+39 x^2+53 x+45$
• $y^2=65 x^6+96 x^5+64 x^4+x^3+112 x^2+70 x+84$
• $y^2=84 x^6+47 x^5+38 x^4+92 x^3+2 x^2+82 x+31$
• $y^2=29 x^6+85 x^5+26 x^4+26 x^3+32 x^2+67 x+1$
• $y^2=21 x^6+64 x^5+111 x^4+9 x^3+82 x^2+59 x+53$
• $y^2=108 x^6+35 x^5+102 x^4+29 x^3+5 x^2+32 x+55$
• $y^2=43 x^6+9 x^5+13 x^4+77 x^3+27 x^2+42 x+8$
• $y^2=103 x^6+25 x^5+43 x^4+68 x^3+39 x^2+44 x+24$
• $y^2=90 x^6+21 x^5+57 x^4+50 x^3+98 x^2+70 x+34$
• $y^2=84 x^6+41 x^5+32 x^4+109 x^3+56 x^2+109 x+90$
• $y^2=69 x^6+41 x^5+15 x^4+2 x^3+73 x^2+60 x$
• $y^2=31 x^6+44 x^5+33 x^4+34 x^3+106 x^2+90 x+10$
• $y^2=103 x^6+35 x^5+66 x^4+107 x^3+79 x^2+93 x+47$
• $y^2=52 x^6+54 x^5+20 x^4+34 x^3+92 x^2+48 x+87$

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 4.0.143964989.1.

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_lv	$2$	(not in LMFDB)