Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 6 x + 60 x^{2} + 207 x^{3} + 1020 x^{4} + 1734 x^{5} + 4913 x^{6}$ |
| Frobenius angles: | $\pm0.518071423272$, $\pm0.564230590399$, $\pm0.655906432749$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1536920811.1 |
| Galois group: | $A_4\times C_2$ |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7941$ | $32137227$ | $112872492549$ | $577454324666211$ | $2870916094910350581$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $24$ | $374$ | $4671$ | $82778$ | $1424064$ | $24140669$ | $410294454$ | $6975733730$ | $118588224312$ | $2015995590914$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
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 6.0.1536920811.1. |
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 |
|---|---|---|
| 3.17.ag_ci_ahz | $2$ | (not in LMFDB) |