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

• Label: 2.113.abe_qz
• 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:	$1 - 30 x + 441 x^{2} - 3390 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.173997398161$, $\pm0.312029122546$
Angle rank:	$2$ (numerical)
Number field:	4.0.60942400.1
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9791$	$162834121$	$2085591131804$	$26589809063948761$	$339460389801675084911$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$12752$	$1445418$	$163080276$	$18424549944$	$2081951954678$	$235260546123288$	$26584442033756068$	$3004041940127248554$	$339456739001248470272$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=85 x^6+108 x^5+57 x^4+70 x^3+14 x^2+86 x+3$
• $y^2=32 x^6+9 x^5+106 x^4+31 x^3+77 x^2+109 x+17$
• $y^2=59 x^6+11 x^5+87 x^4+86 x^3+14 x^2+86 x+4$
• $y^2=75 x^6+109 x^5+62 x^4+94 x^3+14 x^2+35 x+33$
• $y^2=19 x^6+91 x^5+39 x^4+35 x^3+100 x^2+95 x+96$
• $y^2=42 x^6+64 x^5+26 x^4+30 x^3+104 x^2+44 x+96$
• $y^2=41 x^6+30 x^5+56 x^4+94 x^3+72 x^2+75 x+46$
• $y^2=111 x^6+48 x^5+x^4+27 x^3+44 x^2+10 x+65$
• $y^2=77 x^6+57 x^5+76 x^4+74 x^3+13 x^2+110 x+101$
• $y^2=64 x^6+44 x^5+85 x^4+83 x^3+60 x^2+86 x+2$
• $y^2=70 x^6+18 x^5+43 x^4+83 x^3+107 x^2+77 x+17$
• $y^2=80 x^6+92 x^5+47 x^4+79 x^3+45 x^2+93 x+103$
• $y^2=96 x^6+54 x^5+4 x^4+12 x^3+70 x^2+70 x+74$
• $y^2=94 x^6+103 x^5+69 x^4+42 x^3+31 x^2+32 x+27$
• $y^2=84 x^6+50 x^5+27 x^4+75 x^3+9 x^2+43 x+106$
• $y^2=88 x^6+51 x^5+33 x^4+39 x^3+51 x^2+12 x+46$

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 4.0.60942400.1.

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.be_qz	$2$	(not in LMFDB)