Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 25 x^{2} - 77 x^{3} + 121 x^{4} )$ |
| $1 - 13 x + 78 x^{2} - 304 x^{3} + 858 x^{4} - 1573 x^{5} + 1331 x^{6}$ | |
| Frobenius angles: | $\pm0.0530380253560$, $\pm0.140218899004$, $\pm0.477974681599$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $378$ | $1571724$ | $2244302802$ | $3058612625376$ | $4168520769496608$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $109$ | $1265$ | $14265$ | $160714$ | $1774897$ | $19496623$ | $214354241$ | $2357950181$ | $25937800744$ |
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.ah_z 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.ab_ag_ae | $2$ | (not in LMFDB) |
| 3.11.b_ag_e | $2$ | (not in LMFDB) |
| 3.11.n_da_ls | $2$ | (not in LMFDB) |