Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 816 x^{2} - 7348 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.139178331316$, $\pm0.206688739820$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1872128.1 |
Galois group: | $D_{4}$ |
Jacobians: | $20$ |
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
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21314$ | $769392772$ | $21694223366018$ | $605011923167780624$ | $16872075087391615491874$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $27586$ | $4657948$ | $777853926$ | $129893118564$ | $21691976476258$ | $3622557726592516$ | $604967117697540414$ | $101029508528412699484$ | $16871927924761653532866$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=43x^6+139x^5+41x^4+117x^3+112x^2+154x+107$
- $y^2=8x^6+141x^5+57x^4+42x^3+59x^2+46x+104$
- $y^2=149x^6+31x^5+76x^4+150x^3+34x^2+141x+31$
- $y^2=61x^6+54x^5+146x^4+43x^3+76x^2+31x+95$
- $y^2=56x^6+85x^5+84x^4+61x^3+129x^2+60x+47$
- $y^2=163x^6+133x^5+107x^4+79x^3+86x^2+34x+18$
- $y^2=149x^6+26x^5+47x^4+27x^3+17x^2+30x+109$
- $y^2=123x^6+60x^5+90x^4+146x^3+114x^2+37x+54$
- $y^2=6x^6+163x^5+54x^4+83x^3+158x^2+56x+129$
- $y^2=44x^6+74x^5+162x^4+112x^3+3x^2+97x+55$
- $y^2=139x^6+55x^5+93x^4+110x^3+55x^2+109x+123$
- $y^2=56x^6+20x^5+132x^4+127x^3+109x^2+30x+106$
- $y^2=153x^6+9x^5+32x^4+39x^3+52x^2+25x+137$
- $y^2=30x^6+91x^5+120x^4+160x^3+7x^2+117x+79$
- $y^2=137x^6+136x^5+118x^4+17x^3+83x^2+91x+131$
- $y^2=101x^6+90x^5+119x^4+51x^3+130x^2+99x+29$
- $y^2=53x^6+165x^5+107x^4+115x^3+141x^2+162x+85$
- $y^2=80x^6+152x^5+90x^4+142x^3+31x^2+33x+14$
- $y^2=100x^6+67x^5+166x^4+165x^3+163x^2+20x+55$
- $y^2=122x^6+57x^5+83x^4+14x^3+33x^2+70x+148$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The endomorphism algebra of this simple isogeny class is 4.0.1872128.1. |
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 |
---|---|---|
2.167.bs_bfk | $2$ | (not in LMFDB) |