Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 9 x + 49 x^{2} - 153 x^{3} + 289 x^{4}$ |
| Frobenius angles: | $\pm0.191982029838$, $\pm0.413688260814$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.609021.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $177$ | $88677$ | $24814161$ | $6989255109$ | $2016042350352$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $307$ | $5049$ | $83683$ | $1419894$ | $24145747$ | $410396121$ | $6975832771$ | $118586980233$ | $2015988569182$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+2x^5+14x^4+12x^3+6x+14$
- $y^2=6x^6+6x^5+16x^4+x^3+2x^2+8x+13$
- $y^2=6x^6+6x^5+15x^4+2x^3+x^2+x$
- $y^2=x^6+8x^5+12x^4+13x^3+11x^2+8x+15$
- $y^2=14x^6+10x^5+13x^4+15x^3+12x^2+x+10$
- $y^2=12x^6+16x^5+11x^4+15x^3+11x^2+14x$
- $y^2=14x^6+13x^5+12x^4+x^3+16x^2+13x+6$
- $y^2=14x^6+14x^5+10x^4+2x^2+6x+6$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{17}$.
Endomorphism algebra over $\F_{17}$| The endomorphism algebra of this simple isogeny class is 4.0.609021.1. |
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 |
|---|---|---|
| 2.17.j_bx | $2$ | (not in LMFDB) |