Invariants
Base field: | $\F_{23}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 22 x + 223 x^{2} - 1347 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
Frobenius angles: | $\pm0.0394215835568$, $\pm0.175002735951$, $\pm0.351893565228$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.1392115799.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4513$ | $137768351$ | $1805348874844$ | $21914201142006719$ | $266505266925446872048$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $2$ | $492$ | $12197$ | $279836$ | $6433207$ | $148019145$ | $3404825216$ | $78311319396$ | $1801153175195$ | $41426497145507$ |
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 6.0.1392115799.1. |
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 |
---|---|---|
3.23.w_ip_bzv | $2$ | (not in LMFDB) |