Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 13 x + 81 x^{2} - 324 x^{3} + 891 x^{4} - 1573 x^{5} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.0329532391161$, $\pm0.203794694889$, $\pm0.447810262494$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.251429824.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $394$ | $1660316$ | $2341108600$ | $3093241761904$ | $4164698578969294$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $115$ | $1322$ | $14431$ | $160569$ | $1772908$ | $19490631$ | $214319919$ | $2357708858$ | $25936918275$ |
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 $\F_{11}$.
Endomorphism algebra over $\F_{11}$| The endomorphism algebra of this simple isogeny class is 6.0.251429824.2. |
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 |
|---|---|---|
| 3.11.n_dd_mm | $2$ | (not in LMFDB) |