Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 881 x^{2} - 7849 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0206575628157$, $\pm0.193645168874$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.270333.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20875$ | $765423625$ | $21677299959625$ | $604958138129858125$ | $16871932344663363070000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $121$ | $27443$ | $4654315$ | $777784779$ | $129892019636$ | $21691961114951$ | $3622557531209717$ | $604967115371230051$ | $101029508501849574715$ | $16871927924467500538718$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=118x^6+129x^5+9x^4+19x^3+26x^2+106x+156$
- $y^2=138x^6+120x^5+50x^4+125x^3+69x^2+107x+85$
- $y^2=99x^6+67x^5+154x^4+110x^3+115x^2+154x+55$
- $y^2=90x^6+97x^5+2x^4+39x^3+164x^2+138x+22$
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 4.0.270333.1. |
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.bv_bhx | $2$ | (not in LMFDB) |