Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 4 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ |
| $1 - 7 x + 34 x^{2} - 77 x^{3} + 121 x^{4}$ | |
| Frobenius angles: | $\pm0.293962833700$, $\pm0.350615407277$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $72$ | $17280$ | $1965600$ | $218488320$ | $25857660312$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $5$ | $141$ | $1472$ | $14921$ | $160555$ | $1767078$ | $19477225$ | $214369681$ | $2358076352$ | $25937734701$ |
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 isogeny class factors as 1.11.ae $\times$ 1.11.ad and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
|---|---|---|
| 2.11.ab_k | $2$ | 2.121.t_mi |
| 2.11.b_k | $2$ | 2.121.t_mi |
| 2.11.h_bi | $2$ | 2.121.t_mi |