Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 7 x + 44 x^{2} - 239 x^{3} + 836 x^{4} - 2527 x^{5} + 6859 x^{6}$ |
| Frobenius angles: | $\pm0.111837004331$, $\pm0.451697199115$, $\pm0.592698231346$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.70415248979.1 |
| Galois group: | $S_4\times C_2$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4967$ | $52218071$ | $316396469504$ | $2196468615558051$ | $15190590284713057577$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $13$ | $401$ | $6724$ | $129325$ | $2477643$ | $47058908$ | $893917009$ | $16983897877$ | $322688286460$ | $6131066312961$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
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 6.0.70415248979.1. |
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.h_bs_jf | $2$ | (not in LMFDB) |