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

• Label: 2.113.abl_vr
• 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:	$1 - 37 x + 563 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0669838825484$, $\pm0.224024016429$
Angle rank:	$2$ (numerical)
Number field:	4.0.1646253.1
Galois group:	$D_{4}$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9115$	$159977365$	$2080937883355$	$26585612034553525$	$339458909531147297200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$77$	$12527$	$1442195$	$163054539$	$18424469602$	$2081952234479$	$235260538531711$	$26584441706699251$	$3004041935623043825$	$339456738984121259582$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=10x^6+19x^5+51x^4+30x^3+4x^2+72x+9$
• $y^2=78x^6+52x^5+36x^4+25x^3+16x^2+92x+16$
• $y^2=17x^6+52x^5+44x^4+93x^3+77x^2+102x+107$
• $y^2=104x^6+106x^5+71x^4+67x^3+12x^2+104x+78$
• $y^2=42x^6+104x^5+79x^4+8x^3+86x^2+73x+55$
• $y^2=15x^6+23x^5+108x^4+84x^3+110x^2+107x+29$
• $y^2=12x^6+4x^5+45x^4+26x^3+x^2+24x+25$
• $y^2=67x^6+53x^5+34x^4+105x^3+103x^2+14x+39$
• $y^2=25x^6+45x^5+104x^4+62x^3+57x^2+68x+107$
• $y^2=91x^6+44x^5+16x^4+6x^3+x^2+55x+107$

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 4.0.1646253.1.

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.bl_vr	$2$	(not in LMFDB)