Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 15 x + 105 x^{2} - 439 x^{3} + 1155 x^{4} - 1815 x^{5} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.0556623249738$, $\pm0.201555355312$, $\pm0.344091470130$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.4612383.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $323$ | $1570103$ | $2415897557$ | $3161058537943$ | $4171399934792653$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $107$ | $1365$ | $14747$ | $160827$ | $1769735$ | $19484112$ | $214364627$ | $2357959641$ | $25937219327$ |
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 6.0.4612383.1. |
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 |
|---|---|---|
| 3.11.p_eb_qx | $2$ | (not in LMFDB) |