Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 18 x + 152 x^{2} - 781 x^{3} + 2584 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
| Frobenius angles: | $\pm0.0444297450448$, $\pm0.192557823858$, $\pm0.379354628746$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.825389491.2 |
| Galois group: | $S_4\times C_2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1649$ | $22510499$ | $119376414833$ | $582011675415379$ | $2858957755494151289$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $270$ | $4947$ | $83434$ | $1418140$ | $24133317$ | $410353650$ | $6975829026$ | $118587386472$ | $2015988380530$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
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 6.0.825389491.2. |
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.s_fw_beb | $2$ | (not in LMFDB) |