Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 10 x + 51 x^{2} - 173 x^{3} + 408 x^{4} - 640 x^{5} + 512 x^{6}$ |
Frobenius angles: | $\pm0.0539581045269$, $\pm0.264575029509$, $\pm0.465523086978$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.309961175.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 3 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $149$ | $267455$ | $137122763$ | $67196731475$ | $34934051727149$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $67$ | $524$ | $4007$ | $32534$ | $262144$ | $2095470$ | $16762519$ | $134189057$ | $1073809632$ |
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 $\F_{2^{3}}$.
Endomorphism algebra over $\F_{2^{3}}$The endomorphism algebra of this simple isogeny class is 6.0.309961175.1. |
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 |
---|---|---|
3.8.k_bz_gr | $2$ | (not in LMFDB) |