Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 11 x + 61 x^{2} + 234 x^{3} + 671 x^{4} + 1331 x^{5} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.487578494123$, $\pm0.753947955027$, $\pm0.938682872868$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.302352320.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3640$ | $1776320$ | $2394814240$ | $3101568404480$ | $4169529832741000$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $123$ | $1352$ | $14471$ | $160753$ | $1773276$ | $19497179$ | $214301007$ | $2357974424$ | $25937794763$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobian of 1 hyperelliptic curve, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:
- $y^2=3 x^8+7 x^7+5 x^6+9 x^5+4 x^4+2 x^3+2 x+1$
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 6.0.302352320.1. |
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.al_cj_aja | $2$ | (not in LMFDB) |