# Properties

 Label 2.107.abo_xq Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $( 1 - 20 x + 107 x^{2} )^{2}$ Frobenius angles: $\pm0.0823304377774$, $\pm0.0823304377774$ Angle rank: $1$ (numerical) Jacobians: 3

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 3 curves, and hence is principally polarizable:

• $y^2=93x^6+94x^5+39x^4+68x^3+39x^2+94x+93$
• $y^2=58x^6+47x^4+47x^2+58$
• $y^2=5x^6+98x^4+98x^2+5$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7744 126877696 1496864159296 17178795458953216 196713315249072998464 2252191449954175912247296 25785343434737831981758866496 295216379162865095316382679040000 3379932282580397596266764811466283584 38696844634240784758505023714179857514496

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 68 11078 1221884 131056206 14025387508 1500730259222 160578159683884 17181862048951198 1838459216144938148 196715135776634581478

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.au 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-7})$$$)$
All geometric endomorphisms are defined over $\F_{107}$.

## 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 2.107.a_ahe $2$ (not in LMFDB) 2.107.bo_xq $2$ (not in LMFDB) 2.107.u_lh $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.a_ahe $2$ (not in LMFDB) 2.107.bo_xq $2$ (not in LMFDB) 2.107.u_lh $3$ (not in LMFDB) 2.107.a_he $4$ (not in LMFDB) 2.107.au_lh $6$ (not in LMFDB)