Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 6 x + 36 x^{2} + 113 x^{3} + 396 x^{4} + 726 x^{5} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.431745718726$, $\pm0.659408897168$, $\pm0.719905918957$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.243878931.1 |
| Galois group: | $A_4\times C_2$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2609$ | $2397671$ | $2196697121$ | $3174662661931$ | $4164986364960259$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $18$ | $158$ | $1239$ | $14810$ | $160578$ | $1768241$ | $19507884$ | $214360802$ | $2357755332$ | $25937604818$ |
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 $\F_{11}$.
Endomorphism algebra over $\F_{11}$| The endomorphism algebra of this simple isogeny class is 6.0.243878931.1. |
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.ag_bk_aej | $2$ | (not in LMFDB) |