Invariants
| Base field: | $\F_{167}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 48 x + 908 x^{2} - 8016 x^{3} + 27889 x^{4}$ |
| Frobenius angles: | $\pm0.0582449944782$, $\pm0.161602454123$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.223488.6 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20734$ | $764296708$ | $21673863449518$ | $604954103401290384$ | $16871947932450251046574$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $120$ | $27402$ | $4653576$ | $777779590$ | $129892139640$ | $21691966626186$ | $3622557662472456$ | $604967117737605310$ | $101029508536905351864$ | $16871927924903026734762$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=38x^6+25x^5+95x^4+19x^3+91x^2+97x+56$
- $y^2=120x^6+3x^5+28x^4+33x^3+77x^2+139x+163$
- $y^2=143x^6+94x^5+103x^4+153x^3+26x^2+108x+81$
- $y^2=129x^6+23x^5+70x^4+165x^3+98x^2+151x+4$
- $y^2=14x^6+17x^5+30x^4+31x^3+21x^2+128x+60$
- $y^2=19x^6+68x^5+134x^4+130x^3+39x^2+9x+41$
- $y^2=75x^6+155x^5+96x^4+96x^3+63x^2+51x+55$
- $y^2=106x^6+106x^5+19x^4+5x^3+40x^2+66x+77$
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 4.0.223488.6. |
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.bw_biy | $2$ | (not in LMFDB) |