Invariants
| Base field: | $\F_{3^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 5 x + 9 x^{2} )( 1 - 9 x + 37 x^{2} - 81 x^{3} + 81 x^{4} )$ |
| $1 - 14 x + 91 x^{2} - 347 x^{3} + 819 x^{4} - 1134 x^{5} + 729 x^{6}$ | |
| Frobenius angles: | $\pm0.114191348093$, $\pm0.186429498677$, $\pm0.309392441858$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 1 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $145$ | $454575$ | $407933140$ | $291655774575$ | $207683952643600$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-4$ | $68$ | $767$ | $6772$ | $59561$ | $532289$ | $4785224$ | $43058692$ | $387469523$ | $3486896423$ |
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 $\F_{3^{2}}$.
Endomorphism algebra over $\F_{3^{2}}$| The isogeny class factors as 1.9.af $\times$ 2.9.aj_bl 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 |
|---|---|---|
| 3.9.ae_b_x | $2$ | (not in LMFDB) |
| 3.9.e_b_ax | $2$ | (not in LMFDB) |
| 3.9.o_dn_nj | $2$ | (not in LMFDB) |