# Properties

 Label 2.107.abj_tv 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: $1 - 35 x + 515 x^{2} - 3745 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0940700217071$, $\pm0.237116005334$ Angle rank: $2$ (numerical) Number field: 4.0.3149181.2 Galois group: $D_{4}$ Jacobians: 16

This isogeny class is simple and geometrically 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 16 curves, and hence is principally polarizable:

• $y^2=7x^6+23x^5+81x^4+21x^3+20x^2+87x+25$
• $y^2=79x^6+73x^5+37x^4+67x^3+40x^2+94x+61$
• $y^2=19x^6+70x^5+52x^4+106x^3+28x^2+34x+1$
• $y^2=5x^6+18x^5+105x^4+49x^3+55x^2+9x+78$
• $y^2=53x^6+32x^5+78x^4+14x^3+17x^2+105x+69$
• $y^2=15x^6+98x^5+57x^4+2x^3+50x^2+21x+10$
• $y^2=51x^6+15x^5+42x^4+72x^3+4x^2+91x+6$
• $y^2=74x^6+9x^5+28x^4+55x^3+88x^2+101x+38$
• $y^2=95x^6+85x^5+41x^4+28x^3+105x^2+92x+25$
• $y^2=32x^6+92x^5+86x^4+74x^3+29x^2+41x+105$
• $y^2=65x^6+64x^5+59x^4+106x^3+100x^2+14x+26$
• $y^2=15x^6+48x^5+106x^4+13x^3+x^2+95x+29$
• $y^2=35x^5+46x^4+22x^3+106x^2+53x+50$
• $y^2=32x^6+93x^5+37x^4+96x^3+45x^2+72x+7$
• $y^2=20x^6+23x^5+37x^4+89x^3+3x^2+49x+54$
• $y^2=46x^6+104x^5+43x^4+48x^3+100x^2+86x+106$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8185 128872825 1500688016755 17183686623518125 196717600036042370800 2252193212251610993585425 25785341487180839316840231895 295216373796844595511525224743125 3379932275600495426409710421947024965 38696844628111358827450621961597123680000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 73 11255 1225009 131093523 14025693008 1500731433515 160578147555479 17181861736643923 1838459212348333843 196715135745475688150

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.3149181.2.
All geometric endomorphisms are defined over $\F_{107}$.

## 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 2.107.bj_tv $2$ (not in LMFDB)