# Properties

 Label 2.113.abo_yb Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $( 1 - 21 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.148111132014$ Angle rank: $2$ (numerical) Jacobians: 6

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8835 158632425 2078261714880 26582261508455625 339456624762272208675 4334525200255968255283200 55347529339009214603127816195 706732557219286144429582719455625 9024267968714751212474896122098619840 115230877647920668089776360096237545835625

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

## Decomposition and endomorphism algebra

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

## 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)