Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - x + 17 x^{2} - 35 x^{3} + 187 x^{4} - 121 x^{5} + 1331 x^{6}$ |
| Frobenius angles: | $\pm0.238916790429$, $\pm0.543896157017$, $\pm0.646111072817$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.75024047.1 |
| 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 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1379$ | $2334647$ | $2262402569$ | $3159171946343$ | $4223377172474089$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $11$ | $155$ | $1277$ | $14739$ | $162821$ | $1771451$ | $19475992$ | $214342787$ | $2357871911$ | $25937336835$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 13 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:
- $y^2=7 x^8+4 x^7+9 x^6+x^4+8 x^3+4 x^2+9 x+1$
- $y^2=10 x^8+3 x^7+10 x^6+3 x^5+4 x^4+3 x^3+5 x^2+6 x+10$
- $y^2=6 x^8+x^7+8 x^6+7 x^5+x^4+7 x^3+5 x^2+2 x+9$
- $y^2=8 x^8+8 x^7+2 x^6+10 x^5+3 x^4+8 x^3+8 x^2+5 x+2$
- $y^2=2 x^8+6 x^7+x^6+2 x^5+9 x^4+10 x^3+10 x^2+6 x+8$
- $y^2=8 x^8+6 x^7+8 x^6+10 x^5+4 x^4+7 x^2+8 x+3$
- $y^2=x^8+7 x^7+9 x^6+2 x^5+2 x^4+9 x^3+10 x^2+9 x+3$
- $y^2=4 x^8+8 x^7+2 x^6+2 x^4+5 x^3+7 x^2+4 x+10$
- $y^2=3 x^8+10 x^7+8 x^6+3 x^5+9 x^4+10 x^3+9 x^2+2 x+10$
- $y^2=3 x^8+6 x^7+2 x^6+4 x^5+4 x^4+9 x^3+3 x+1$
- $y^2=7 x^8+7 x^7+7 x^6+10 x^5+10 x^4+4 x^3+8 x^2+10 x+7$
- $y^2=3 x^8+2 x^7+x^6+6 x^5+8 x^4+8 x^3+8 x^2+5 x+8$
- $y^2=5 x^8+9 x^7+6 x^5+8 x^4+2 x^3+8 x^2+3 x+7$
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 6.0.75024047.1. |
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.b_r_bj | $2$ | (not in LMFDB) |