Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 5 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ |
| $1 - 9 x + 42 x^{2} - 99 x^{3} + 121 x^{4}$ | |
| Frobenius angles: | $\pm0.228229222880$, $\pm0.293962833700$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $56$ | $15232$ | $1920800$ | $220864000$ | $26066804456$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $3$ | $125$ | $1440$ | $15081$ | $161853$ | $1770662$ | $19475823$ | $214320721$ | $2357894880$ | $25937537405$ |
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.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.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.11.ab_c | $2$ | 2.121.d_iq |
| 2.11.b_c | $2$ | 2.121.d_iq |
| 2.11.j_bq | $2$ | 2.121.d_iq |