Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 17 x^{2} )( 1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4} )$ |
| $1 - 20 x + 183 x^{2} - 967 x^{3} + 3111 x^{4} - 5780 x^{5} + 4913 x^{6}$ | |
| Frobenius angles: | $\pm0.125047581931$, $\pm0.177280642489$, $\pm0.273653339326$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1441$ | $21578975$ | $120541102528$ | $588979672601375$ | $2870711946547676176$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $256$ | $4993$ | $84428$ | $1423963$ | $24149917$ | $410366472$ | $6975828532$ | $118588228711$ | $2015995680111$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{17}$.
Endomorphism algebra over $\F_{17}$| The isogeny class factors as 1.17.ah $\times$ 2.17.an_cx and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
|---|---|---|
| 3.17.ag_b_df | $2$ | (not in LMFDB) |
| 3.17.g_b_adf | $2$ | (not in LMFDB) |
| 3.17.u_hb_blf | $2$ | (not in LMFDB) |