Invariants
Base field: | $\F_{2}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6}$ |
Frobenius angles: | $\pm0.147012170705$, $\pm0.341962716420$, $\pm0.600633654388$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.465831.1 |
Galois group: | $A_4\times C_2$ |
Jacobians: | $0$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3$ | $153$ | $513$ | $5661$ | $46923$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $8$ | $9$ | $20$ | $45$ | $59$ | $126$ | $332$ | $594$ | $983$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$The endomorphism algebra of this simple isogeny class is 6.0.465831.1. |
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 |
---|---|---|
3.2.d_g_j | $2$ | 3.4.d_g_h |