Invariants
| Base field: | $\F_{13}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 18 x^{2} + 37 x^{3} + 234 x^{4} + 2197 x^{6}$ |
| Frobenius angles: | $\pm0.377036888638$, $\pm0.383817837377$, $\pm0.762213001637$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.318884283.1 |
| Galois group: | $A_4\times C_2$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2487$ | $6001131$ | $11148905151$ | $23535049520739$ | $50728603480284747$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $14$ | $206$ | $2309$ | $28850$ | $367964$ | $4822277$ | $62771828$ | $815789042$ | $10604782868$ | $137857007606$ |
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 $\F_{13}$.
Endomorphism algebra over $\F_{13}$| The endomorphism algebra of this simple isogeny class is 6.0.318884283.1. |
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.a_s_abl | $2$ | (not in LMFDB) |