Invariants
Base field: | $\F_{7}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 11 x + 59 x^{2} - 195 x^{3} + 413 x^{4} - 539 x^{5} + 343 x^{6}$ |
Frobenius angles: | $\pm0.0413211978612$, $\pm0.265511145545$, $\pm0.363643463851$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.400967.1 |
Galois group: | $A_4\times C_2$ |
Isomorphism classes: | 1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $71$ | $110831$ | $43933877$ | $13983436439$ | $4666007907401$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-3$ | $47$ | $375$ | $2427$ | $16517$ | $116387$ | $821048$ | $5762531$ | $40352631$ | $282467967$ |
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 6.0.400967.1. |
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 |
---|---|---|
3.7.l_ch_hn | $2$ | (not in LMFDB) |