Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 21 x + 197 x^{2} - 1085 x^{3} + 3743 x^{4} - 7581 x^{5} + 6859 x^{6}$ |
| Frobenius angles: | $\pm0.0244838694525$, $\pm0.0919107140824$, $\pm0.350275104257$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.400967.1 |
| Galois group: | $A_4\times C_2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2113$ | $41176031$ | $317707854919$ | $2200473161067623$ | $15147133075884914623$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $315$ | $6755$ | $129563$ | $2470549$ | $47022783$ | $893837440$ | $16983737715$ | $322688804207$ | $6131067450095$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain 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 6.0.400967.1. |
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.v_hp_bpt | $2$ | (not in LMFDB) |