Invariants
| Base field: | $\F_{167}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 47 x + 885 x^{2} - 7849 x^{3} + 27889 x^{4}$ |
| Frobenius angles: | $\pm0.0985019100004$, $\pm0.166692854905$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.258725.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20879$ | $765653809$ | $21679931364101$ | $604974641631791261$ | $16872006825207323079184$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $121$ | $27451$ | $4654879$ | $777805995$ | $129892593036$ | $21691973538487$ | $3622557758315785$ | $604967118961235139$ | $101029508551333260763$ | $16871927925058514432286$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=70 x^6+160 x^5+10 x^4+88 x^3+18 x^2+14 x+35$
- $y^2=4 x^6+106 x^5+13 x^4+135 x^3+26 x^2+85 x+85$
- $y^2=136 x^6+165 x^5+95 x^4+131 x^3+88 x^2+15 x+156$
- $y^2=155 x^6+8 x^5+91 x^4+32 x^3+53 x^2+138 x+51$
- $y^2=73 x^6+44 x^5+141 x^4+156 x^3+110 x^2+142 x+166$
- $y^2=58 x^6+4 x^5+69 x^4+28 x^3+156 x+153$
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 4.0.258725.1. |
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_bib | $2$ | (not in LMFDB) |