Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$ |
| Frobenius angles: | $\pm0.147872872551$, $\pm0.436753511906$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.971388.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $10$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $174$ | $86652$ | $24410808$ | $6955729344$ | $2015469561774$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $301$ | $4968$ | $83281$ | $1419489$ | $24150418$ | $410418801$ | $6975900769$ | $118587552984$ | $2015992942141$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):
- $y^2=11 x^6+9 x^5+5 x^4+16 x^3+5 x^2+10$
- $y^2=14 x^5+11 x^4+11 x^3+7 x^2+14 x+7$
- $y^2=12 x^6+5 x^5+9 x^4+12 x^3+9 x^2+15 x+7$
- $y^2=11 x^6+2 x^5+10 x^4+6 x^3+6 x^2+14 x+6$
- $y^2=6 x^6+2 x^5+14 x^4+16 x^3+4 x^2+2 x+7$
- $y^2=14 x^6+2 x^5+4 x^4+14 x^3+11 x+9$
- $y^2=7 x^5+x^4+9 x^3+6 x^2+7 x+1$
- $y^2=2 x^6+7 x^5+7 x^4+10 x^3+10 x^2+10$
- $y^2=14 x^6+16 x^5+6 x^4+15 x^3+13 x^2+13 x+11$
- $y^2=11 x^6+11 x^5+2 x^4+12 x^3+3 x^2+4 x+14$
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 4.0.971388.2. |
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_bu | $2$ | (not in LMFDB) |