Invariants
Base field: | $\F_{7}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 9 x + 38 x^{2} - 112 x^{3} + 266 x^{4} - 441 x^{5} + 343 x^{6}$ |
Frobenius angles: | $\pm0.0283467889665$, $\pm0.193732293337$, $\pm0.536888824784$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.30088184.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 2 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $86$ | $104060$ | $36096350$ | $13240594400$ | $4794339367136$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $45$ | $305$ | $2297$ | $16974$ | $118185$ | $821547$ | $5757537$ | $40346945$ | $282434600$ |
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 $\F_{7}$.
Endomorphism algebra over $\F_{7}$The endomorphism algebra of this simple isogeny class is 6.0.30088184.1. |
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 |
---|---|---|
3.7.j_bm_ei | $2$ | (not in LMFDB) |