Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 36 x^{2} - 88 x^{3} + 121 x^{4} )$ |
| $1 - 14 x + 95 x^{2} - 392 x^{3} + 1045 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
| Frobenius angles: | $\pm0.140218899004$, $\pm0.196063835166$, $\pm0.372536541753$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $372$ | $1700784$ | $2487136572$ | $3191106184704$ | $4191399146410932$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $116$ | $1402$ | $14884$ | $161598$ | $1774196$ | $19502362$ | $214409020$ | $2357985310$ | $25936992916$ |
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 $\times$ 2.11.ai_bk 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 |
|---|---|---|
| 3.11.ac_ab_bo | $2$ | (not in LMFDB) |
| 3.11.c_ab_abo | $2$ | (not in LMFDB) |
| 3.11.o_dr_pc | $2$ | (not in LMFDB) |