# Properties

 Label 2.107.abi_sy 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: $1 - 34 x + 492 x^{2} - 3638 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0604166695618$, $\pm0.269957969854$ Angle rank: $2$ (numerical) Number field: 4.0.7101248.1 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:

• $y^2=50x^6+79x^5+2x^4+99x^3+67x^2+51x+55$
• $y^2=77x^6+94x^5+71x^4+102x^3+28x^2+24x+98$
• $y^2=16x^6+73x^5+75x^4+47x^3+33x^2+51x+7$
• $y^2=91x^6+81x^5+56x^4+90x^3+8x^2+18x+72$
• $y^2=77x^6+12x^5+52x^4+85x^3+76x^2+60x+26$
• $y^2=98x^6+37x^5+44x^4+72x^3+2x^2+60x+68$
• $y^2=23x^5+11x^4+104x^3+17x^2+22x+80$
• $y^2=78x^6+9x^5+85x^4+15x^3+86x^2+85x+73$
• $y^2=91x^6+50x^5+52x^4+81x^3+51x^2+24x+45$
• $y^2=87x^6+65x^5+78x^4+41x^3+37x^2+77x+106$
• $y^2=77x^6+98x^5+31x^4+102x^3+95x^2+52x+87$
• $y^2=92x^6+75x^5+75x^4+6x^3+22x^2+42x+26$
• $y^2=27x^6+42x^5+88x^4+43x^3+60x^2+8x+11$
• $y^2=60x^6+66x^5+80x^4+80x^3+105x^2+75x+60$
• $y^2=55x^6+3x^5+40x^4+99x^3+57x^2+87x+75$
• $y^2=87x^6+2x^5+104x^4+61x^3+97x^2+34x+18$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8270 129127780 1500687737990 17182592067592400 196714710853131425350 2252188698732175168306180 25785336698284566441170087630 295216370671288780547419872588800 3379932275322273764399379976901735870 38696844629873053219252588947959445808900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11278 1225010 131085174 14025487014 1500728425966 160578117732638 17181861554733726 1838459212196999690 196715135754431249118

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.7101248.1.
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_sy $2$ (not in LMFDB)