Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 12 x + 69 x^{2} - 243 x^{3} + 552 x^{4} - 768 x^{5} + 512 x^{6}$ |
| Frobenius angles: | $\pm0.0669770653565$, $\pm0.221003101311$, $\pm0.377685533829$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.3300183.1 |
| Galois group: | $A_4\times C_2$ |
| Isomorphism classes: | 3 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $111$ | $239427$ | $141357501$ | $69231035331$ | $34993719389751$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $59$ | $540$ | $4127$ | $32592$ | $261680$ | $2097708$ | $16780199$ | $134209143$ | $1073673284$ |
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 endomorphism algebra of this simple isogeny class is 6.0.3300183.1. |
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.m_cr_jj | $2$ | (not in LMFDB) |