Invariants
| Base field: | $\F_{13}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 16 x + 120 x^{2} - 543 x^{3} + 1560 x^{4} - 2704 x^{5} + 2197 x^{6}$ |
| Frobenius angles: | $\pm0.0186782147920$, $\pm0.208870362755$, $\pm0.359149016839$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.9709203.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $615$ | $4391715$ | $10769211495$ | $23323805483475$ | $51056734370604075$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $154$ | $2233$ | $28594$ | $370358$ | $4821877$ | $62736574$ | $815703202$ | $10604283508$ | $137856949034$ |
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 6.0.9709203.1. |
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.q_eq_ux | $2$ | (not in LMFDB) |