Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 3 x - 12 x^{2} - 164 x^{3} - 228 x^{4} + 1083 x^{5} + 6859 x^{6}$ |
| Frobenius angles: | $\pm0.0349688934801$, $\pm0.670128790787$, $\pm0.810922246671$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.189631638216.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7542$ | $42974316$ | $306282437622$ | $2217645571480416$ | $15154401926880276192$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $23$ | $329$ | $6503$ | $130577$ | $2471738$ | $47033861$ | $893831045$ | $16983496625$ | $322686615209$ | $6131062268744$ |
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 $\F_{19}$.
Endomorphism algebra over $\F_{19}$| The endomorphism algebra of this simple isogeny class is 6.0.189631638216.1. |
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 |
|---|---|---|
| 3.19.ad_am_gi | $2$ | (not in LMFDB) |