Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 11 x + 82 x^{2} - 431 x^{3} + 1558 x^{4} - 3971 x^{5} + 6859 x^{6}$ |
| Frobenius angles: | $\pm0.118811287197$, $\pm0.421397608704$, $\pm0.472525336687$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1193220400.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4087$ | $52775431$ | $326643551764$ | $2194166250926275$ | $15160477540737208597$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $405$ | $6942$ | $129189$ | $2472729$ | $47067528$ | $894016391$ | $16983722229$ | $322687107318$ | $6131069714505$ |
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 6.0.1193220400.1. |
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.l_de_qp | $2$ | (not in LMFDB) |