Invariants
| Base field: | $\F_{167}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 48 x + 907 x^{2} - 8016 x^{3} + 27889 x^{4}$ |
| Frobenius angles: | $\pm0.0298610959797$, $\pm0.169479775008$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.145296.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20733$ | $764239113$ | $21673191542004$ | $604949758123365369$ | $16871927482105786543893$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $120$ | $27400$ | $4653432$ | $777774004$ | $129891982200$ | $21691963020310$ | $3622557591581160$ | $604967116504131364$ | $101029508517559028904$ | $16871927924626240219000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=69 x^6+122 x^5+32 x^4+106 x^3+39 x^2+144 x+149$
- $y^2=102 x^6+107 x^5+37 x^4+38 x^3+153 x^2+5 x+79$
- $y^2=79 x^6+26 x^5+119 x^4+14 x^3+4 x^2+57 x+6$
- $y^2=133 x^6+152 x^5+64 x^4+136 x^3+92 x^2+111 x+35$
- $y^2=126 x^6+3 x^5+88 x^4+109 x^3+21 x^2+135 x+143$
- $y^2=127 x^6+161 x^5+108 x^4+118 x^3+26 x^2+77 x+81$
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 4.0.145296.1. |
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.bw_bix | $2$ | (not in LMFDB) |