Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ |
| $1 - 15 x + 107 x^{2} - 450 x^{3} + 1177 x^{4} - 1815 x^{5} + 1331 x^{6}$ | |
| Frobenius angles: | $\pm0.140218899004$, $\pm0.228229222880$, $\pm0.293962833700$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $336$ | $1645056$ | $2523931200$ | $3244050432000$ | $4210466656559856$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $111$ | $1422$ | $15127$ | $162327$ | $1773000$ | $19484637$ | $214347887$ | $2357960922$ | $25937634831$ |
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.ag $\times$ 1.11.af $\times$ 1.11.ae 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.