Invariants
| Base field: | $\F_{13}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 15 x + 109 x^{2} - 487 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
| Frobenius angles: | $\pm0.103362670615$, $\pm0.212954520112$, $\pm0.386876328178$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.319611111.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $687$ | $4644807$ | $10945226979$ | $23430789293991$ | $51194738741758707$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $163$ | $2267$ | $28723$ | $371359$ | $4828915$ | $62768852$ | $815800099$ | $10604513195$ | $137857868003$ |
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 $\F_{13}$.
Endomorphism algebra over $\F_{13}$| The endomorphism algebra of this simple isogeny class is 6.0.319611111.1. |
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 |
|---|---|---|
| 3.13.p_ef_st | $2$ | (not in LMFDB) |