Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 7 x + 44 x^{2} + 179 x^{3} + 748 x^{4} + 2023 x^{5} + 4913 x^{6}$ |
| Frobenius angles: | $\pm0.388433391500$, $\pm0.622331457632$, $\pm0.804538070856$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1733460656.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7915$ | $27678755$ | $117522964780$ | $584948000036075$ | $2857416301207937075$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $25$ | $329$ | $4870$ | $83853$ | $1417375$ | $24134408$ | $410330435$ | $6976048517$ | $118588171330$ | $2015986266189$ |
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 6.0.1733460656.1. |
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.ah_bs_agx | $2$ | (not in LMFDB) |