# Properties

 Label 2.113.abo_yc 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: $( 1 - 20 x + 113 x^{2} )^{2}$ Frobenius angles: $\pm0.110150159186$, $\pm0.110150159186$ Angle rank: $1$ (numerical) Jacobians: 5

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 5 curves, and hence is principally polarizable:

• $y^2=71x^6+84x^5+70x^4+30x^3+70x^2+84x+71$
• $y^2=64x^6+60x^5+76x^4+93x^3+81x^2+70x+38$
• $y^2=59x^6+54x^5+72x^4+39x^3+72x^2+54x+59$
• $y^2=17x^6+103x^5+26x^4+84x^3+66x^2+102$
• $y^2=32x^6+90x^4+90x^2+32$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8836 158659216 2078435455684 26582897240805376 339458327210053271236 4334528918811578125200016 55347536324836887753497270404 706732568824316317347730268160000 9024267985987220330078728605189810436 115230877670989670770259870006704555966096

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 12422 1440458 163037886 18424437994 2081954547398 235260594199978 26584442536356478 3004041944914578314 339456739062204502022

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.au 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-13})$$$)$
All geometric endomorphisms are defined over $\F_{113}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.a_ags $2$ (not in LMFDB) 2.113.bo_yc $2$ (not in LMFDB) 2.113.u_lb $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.a_ags $2$ (not in LMFDB) 2.113.bo_yc $2$ (not in LMFDB) 2.113.u_lb $3$ (not in LMFDB) 2.113.a_gs $4$ (not in LMFDB) 2.113.au_lb $6$ (not in LMFDB)