# Properties

 Label 2.107.ac_afc Base field $\F_{107}$ Dimension $2$ $p$-rank $2$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

# Related objects

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $1 - 2 x - 132 x^{2} - 214 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.102347107508$, $\pm0.824658098163$ Angle rank: $2$ (numerical) Number field: 4.0.9655838528.1 Galois group: $D_{4}$ Jacobians: 128

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 128 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=78x^6+20x^5+104x^4+24x^3+52x^2+44x+30$
• $y^2=2x^6+7x^5+72x^4+51x^3+10x^2+80x+84$
• $y^2=80x^6+89x^5+37x^4+x^3+20x^2+7x+17$
• $y^2=32x^6+20x^5+6x^4+52x^3+14x^2+67x+15$
• $y^2=17x^6+84x^5+2x^4+3x^3+37x^2+30x+95$
• $y^2=54x^6+74x^5+103x^4+91x^3+23x^2+58x+34$
• $y^2=65x^6+59x^5+26x^4+104x^3+25x^2+41x+15$
• $y^2=54x^6+66x^5+38x^4+10x^3+31x^2+40x+60$
• $y^2=94x^6+24x^5+44x^4+86x^3+27x^2+7x+100$
• $y^2=63x^6+17x^5+67x^4+6x^3+52x^2+43x+4$
• $y^2=23x^6+77x^5+25x^4+61x^3+103x^2+45x+31$
• $y^2=71x^6+61x^5+8x^4+11x^3+52x^2+x+104$
• $y^2=94x^6+94x^5+49x^4+85x^3+59x^2+14x+101$
• $y^2=57x^6+72x^5+92x^4+77x^3+97x^2+9x+58$
• $y^2=50x^6+48x^5+33x^4+41x^3+90x^2+89x+67$
• $y^2=83x^6+53x^5+86x^4+16x^3+6x^2+37x+26$
• $y^2=15x^6+11x^5+87x^4+88x^3+60x^2+52x+2$
• $y^2=x^6+33x^5+28x^4+67x^3+29x^2+6x+82$
• $y^2=10x^6+96x^5+33x^3+7x^2+65x+56$
• $y^2=101x^6+48x^5+70x^4+98x^3+86x^2+73x+12$
• and 108 more

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $11102$ $128050468$ $1498966516502$ $17182793687228624$ $196712182233607083862$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $106$ $11182$ $1223602$ $131086710$ $14025306726$ $1500733628686$ $160578144435262$ $17181862097992350$ $1838459215707636202$ $196715135736884363262$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.9655838528.1.
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.
TwistExtension degreeCommon base change
2.107.c_afc$2$(not in LMFDB)