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

• Label: 2.113.abo_yb
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$( 1 - 21 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$
	$1 - 40 x + 625 x^{2} - 4520 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0498602789898$, $\pm0.148111132014$
Angle rank:	$2$ (numerical)
Jacobians:	$6$
Isomorphism classes:	8

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8835$	$158632425$	$2078261714880$	$26582261508455625$	$339456624762272208675$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$12420$	$1440338$	$163033988$	$18424345594$	$2081952761310$	$235260564505978$	$26584442099821828$	$3004041939164835314$	$339456738994245908100$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=47x^6+94x^5+76x^3+94x+47$
• $y^2=105x^6+74x^5+110x^4+57x^3+110x^2+74x+105$
• $y^2=20x^6+63x^5+111x^4+106x^3+111x^2+63x+20$
• $y^2=13x^6+40x^5+106x^4+75x^3+106x^2+40x+13$
• $y^2=39x^6+9x^5+69x^4+60x^3+69x^2+9x+39$
• $y^2=39x^6+59x^5+112x^4+102x^3+112x^2+59x+39$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The isogeny class factors as 1.113.av $\times$ 1.113.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.113.av : \(\Q(\sqrt{-11}) \).
• 1.113.at : \(\Q(\sqrt{-91}) \).

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.ac_agr	$2$	(not in LMFDB)
2.113.c_agr	$2$	(not in LMFDB)
2.113.bo_yb	$2$	(not in LMFDB)