Invariants
Base field: | $\F_{5}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6}$ |
Frobenius angles: | $\pm0.0605820805461$, $\pm0.287119770935$, $\pm0.511693182811$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.2419571.1 |
Galois group: | $S_4\times C_2$ |
Jacobians: | $0$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $32$ | $17024$ | $1936928$ | $228053504$ | $30324608512$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $29$ | $125$ | $585$ | $3104$ | $15605$ | $77293$ | $388625$ | $1955159$ | $9779244$ |
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 $\F_{5}$.
Endomorphism algebra over $\F_{5}$The endomorphism algebra of this simple isogeny class is 6.0.2419571.1. |
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 |
---|---|---|
3.5.h_ba_cq | $2$ | 3.25.d_aq_acm |