Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + x + 46 x^{2} + 29 x^{3} + 874 x^{4} + 361 x^{5} + 6859 x^{6}$ |
| Frobenius angles: | $\pm0.378601480297$, $\pm0.529498695743$, $\pm0.629038407068$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.11190299184.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8171$ | $60375519$ | $320317679012$ | $2202003189733491$ | $15188855399934253721$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $21$ | $453$ | $6810$ | $129653$ | $2477361$ | $47038104$ | $893844903$ | $16983889685$ | $322688313546$ | $6131062326153$ |
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 6.0.11190299184.1. |
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.ab_bu_abd | $2$ | (not in LMFDB) |