# Properties

 Label 2.107.abi_td 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: $1 - 34 x + 497 x^{2} - 3638 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.110706537265$, $\pm0.251697673458$ Angle rank: $2$ (numerical) Number field: 4.0.6193728.2 Galois group: $D_{4}$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

• $y^2=21x^6+57x^5+103x^4+40x^3+26x^2+72x+26$
• $y^2=38x^6+23x^5+5x^4+63x^3+59x^2+10x+45$
• $y^2=93x^6+64x^5+36x^4+10x^3+76x^2+25x+32$
• $y^2=53x^6+6x^5+24x^4+4x^3+51x^2+88x+94$
• $y^2=38x^6+23x^5+74x^4+34x^3+70x^2+96x+64$
• $y^2=74x^6+82x^5+91x^4+49x^3+86x^2+77x+39$
• $y^2=5x^6+27x^5+41x^4+8x^3+94x^2+46x+32$
• $y^2=85x^6+38x^5+47x^4+69x^3+61x^2+105x+45$
• $y^2=50x^6+69x^5+68x^4+87x^3+87x^2+84x+43$
• $y^2=62x^6+103x^5+3x^4+92x^3+x^2+49x+45$
• $y^2=63x^6+67x^5+85x^4+24x^3+82x^2+57x+21$
• $y^2=24x^6+80x^5+4x^4+5x^3+27x^2+8x+59$
• $y^2=78x^6+42x^5+13x^4+28x^3+77x^2+106x+26$
• $y^2=50x^6+18x^5+37x^4+51x^3+87x^2+49x+31$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8275 129247225 1501314151300 17184326525505625 196717977417428093875 2252193285443346062035600 25785341613067313032308600475 295216374573109289779847788595625 3379932277365647323374650735729812900 38696844630364802866222577399570576853625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11288 1225520 131098404 14025719914 1500731482286 160578148339438 17181861781823236 1838459213308459520 196715135756931054968

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.6193728.2.
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.bi_td $2$ (not in LMFDB)