Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ |
| $1 - 13 x + 76 x^{2} - 221 x^{3} + 289 x^{4}$ | |
| Frobenius angles: | $\pm0.177280642489$, $\pm0.240632536990$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 3 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $132$ | $79200$ | $24659712$ | $7053552000$ | $2021889165252$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $5$ | $273$ | $5018$ | $84449$ | $1424005$ | $24148926$ | $410345941$ | $6975637441$ | $118587075386$ | $2015990930193$ |
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 $\times$ 1.17.ag 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 |
|---|---|---|
| 2.17.ab_ai | $2$ | (not in LMFDB) |
| 2.17.b_ai | $2$ | (not in LMFDB) |
| 2.17.n_cy | $2$ | (not in LMFDB) |