Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 29 x^{2} + 2 x^{3} + 319 x^{4} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.418735557018$, $\pm0.474097353952$, $\pm0.608338196709$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1541953984.1 |
| Galois group: | $S_4\times C_2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1682$ | $2822396$ | $2369391350$ | $3052714803184$ | $4169704376890202$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $12$ | $180$ | $1338$ | $14236$ | $160762$ | $1772808$ | $19494480$ | $214375644$ | $2357817792$ | $25937066800$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 2 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:
- $y^2=8 x^8+7 x^7+9 x^6+3 x^5+8 x^4+8 x^3+5 x^2+4 x+5$
- $y^2=6 x^8+8 x^6+8 x^5+2 x^3+4 x^2+7 x+7$
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 6.0.1541953984.1. |
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.a_bd_ac | $2$ | (not in LMFDB) |