Invariants
| Base field: | $\F_{11^{2}}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 21 x + 121 x^{2} )^{2}$ |
| $1 - 42 x + 683 x^{2} - 5082 x^{3} + 14641 x^{4}$ | |
| Frobenius angles: | $\pm0.0963413489042$, $\pm0.0963413489042$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $2$ |
This isogeny class is not simple, not primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10201$ | $208600249$ | $3132630965776$ | $45945306460164969$ | $672749035248192022201$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $80$ | $14244$ | $1768286$ | $214338244$ | $25937387600$ | $3138430096878$ | $379749874183760$ | $45949730508044164$ | $5559917322113480846$ | $672749995035625133604$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=9ax^6+6ax^5+5ax^4+7ax^3+5ax^2+6ax+9a$
- $y^2=(2a+3)x^6+(5a+8)x^5+(7a+8)x^4+(5a+4)x^3+(5a+10)x^2+ax+6a+9$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{11^{2}}$.
Endomorphism algebra over $\F_{11^{2}}$| The isogeny class factors as 1.121.av 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-43}) \)$)$ |
Base change
This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{11^{2}}$.
| Subfield | Primitive Model |
| $\F_{11}$ | 2.11.a_av |