Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 6 x + 23 x^{2} - 48 x^{3} + 64 x^{4} )$ |
| $1 - 11 x + 61 x^{2} - 211 x^{3} + 488 x^{4} - 704 x^{5} + 512 x^{6}$ | |
| Frobenius angles: | $\pm0.154919815756$, $\pm0.215051068352$, $\pm0.409556076405$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 24 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $136$ | $270368$ | $148107400$ | $70585514496$ | $35472230211176$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $66$ | $562$ | $4206$ | $33038$ | $263634$ | $2102546$ | $16783262$ | $134189806$ | $1073610786$ |
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.ag_x 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.ab_b_t | $2$ | (not in LMFDB) |
| 3.8.b_b_at | $2$ | (not in LMFDB) |
| 3.8.l_cj_id | $2$ | (not in LMFDB) |