Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 3 x + 8 x^{2} )( 1 - 7 x + 24 x^{2} - 56 x^{3} + 64 x^{4} )$ |
| $1 - 10 x + 53 x^{2} - 184 x^{3} + 424 x^{4} - 640 x^{5} + 512 x^{6}$ | |
| Frobenius angles: | $\pm0.0585111942353$, $\pm0.322067999368$, $\pm0.418160225599$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $156$ | $284544$ | $144165996$ | $67367499264$ | $34451442174396$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $71$ | $551$ | $4015$ | $32079$ | $260711$ | $2097143$ | $16782175$ | $134224607$ | $1073754391$ |
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.ad $\times$ 2.8.ah_y 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.ae_l_abo | $2$ | (not in LMFDB) |
| 3.8.e_l_bo | $2$ | (not in LMFDB) |
| 3.8.k_cb_hc | $2$ | (not in LMFDB) |