Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 22 x + 222 x^{2} - 1337 x^{3} + 5106 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
| Frobenius angles: | $\pm0.0586739858078$, $\pm0.151170230865$, $\pm0.361585258984$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1006556771.2 |
| Galois group: | $S_4\times C_2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4499$ | $137188007$ | $1800065686991$ | $21894088246506971$ | $266486467838989230569$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $490$ | $12161$ | $279578$ | $6432752$ | $148027321$ | $3404919282$ | $78311902642$ | $1801155908972$ | $41426509622670$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 6.0.1006556771.2. |
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 |
|---|---|---|
| 3.23.w_io_bzl | $2$ | (not in LMFDB) |