# Properties

 Label 2.107.abk_us 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: $( 1 - 18 x + 107 x^{2} )^{2}$ Frobenius angles: $\pm0.164078095836$, $\pm0.164078095836$ Angle rank: $1$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=106x^6+100x^5+89x^4+42x^3+9x^2+25x+67$
• $y^2=89x^6+106x^4+106x^2+89$
• $y^2=41x^6+91x^5+76x^4+36x^3+76x^2+91x+41$
• $y^2=62x^6+30x^5+95x^4+89x^3+95x^2+30x+62$
• $y^2=78x^6+90x^5+79x^4+35x^3+81x^2+11x+97$
• $y^2=98x^6+12x^5+86x^4+63x^3+27x^2+105x+21$
• $y^2=97x^6+58x^4+58x^2+97$
• $y^2=59x^6+79x^5+92x^4+27x^3+42x^2+33x+77$
• $y^2=21x^6+7x^5+81x^4+72x^3+27x^2+84x+84$
• $y^2=72x^6+22x^5+9x^3+22x+72$
• $y^2=20x^6+99x^5+73x^4+76x^3+73x^2+99x+20$
• $y^2=49x^6+21x^5+20x^4+58x^3+80x^2+15x+33$
• $y^2=37x^6+67x^5+92x^4+38x^3+92x^2+67x+37$
• $y^2=83x^6+31x^5+17x^4+104x^3+17x^2+31x+83$
• $y^2=20x^6+27x^5+32x^4+91x^3+32x^2+27x+20$
• $y^2=70x^6+35x^5+90x^4+23x^3+56x^2+101x+71$
• $y^2=95x^6+68x^4+68x^2+95$
• $y^2=46x^6+20x^5+14x^4+38x^3+15x^2+35x+21$
• $y^2=101x^6+74x^5+82x^4+42x^3+45x^2+60x+29$
• $y^2=12x^6+32x^5+92x^4+57x^3+92x^2+32x+12$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8100 128595600 1500600500100 17184692972160000 196720749987234502500 2252198934054403712960400 25785348771021852620760524100 295216379858606794227674818560000 3379932276461665888148165602485080100 38696844620138351364900982193687560890000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 72 11230 1224936 131101198 14025917592 1500735246190 160578192915576 17181862089443998 1838459212816753512 196715135704944961150

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-26})$$$)$
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_aeg $2$ (not in LMFDB) 2.107.bk_us $2$ (not in LMFDB) 2.107.s_ij $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.a_aeg $2$ (not in LMFDB) 2.107.bk_us $2$ (not in LMFDB) 2.107.s_ij $3$ (not in LMFDB) 2.107.a_eg $4$ (not in LMFDB) 2.107.as_ij $6$ (not in LMFDB)