Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 6 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
| $1 - 11 x + 64 x^{2} - 187 x^{3} + 289 x^{4}$ | |
| Frobenius angles: | $\pm0.240632536990$, $\pm0.292637436158$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $156$ | $86112$ | $25240176$ | $7065661824$ | $2019105335676$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $7$ | $297$ | $5134$ | $84593$ | $1422047$ | $24132222$ | $410276447$ | $6975515041$ | $118587559918$ | $2015995840857$ |
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.ag $\times$ 1.17.af 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_e | $2$ | (not in LMFDB) |
| 2.17.b_e | $2$ | (not in LMFDB) |
| 2.17.l_cm | $2$ | (not in LMFDB) |