Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 5 x + 19 x^{2} - 40 x^{3} + 64 x^{4} )$ |
| $1 - 10 x + 52 x^{2} - 175 x^{3} + 416 x^{4} - 640 x^{5} + 512 x^{6}$ | |
| Frobenius angles: | $\pm0.154919815756$, $\pm0.224889948753$, $\pm0.460667327867$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 30 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $156$ | $281736$ | $144310608$ | $69654718224$ | $35615923201716$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $69$ | $548$ | $4153$ | $33169$ | $264366$ | $2101483$ | $16772081$ | $134181404$ | $1073706789$ |
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 $\F_{2^{3}}$.
Endomorphism algebra over $\F_{2^{3}}$| The isogeny class factors as 1.8.af $\times$ 2.8.af_t 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 |
|---|---|---|
| 3.8.a_c_ap | $2$ | (not in LMFDB) |
| 3.8.a_c_p | $2$ | (not in LMFDB) |
| 3.8.k_ca_gt | $2$ | (not in LMFDB) |