Invariants
Base field: | $\F_{5}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 7 x + 27 x^{2} - 71 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6}$ |
Frobenius angles: | $\pm0.111887224672$, $\pm0.292466693033$, $\pm0.493752400559$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.39563351.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $35$ | $18935$ | $2147495$ | $238145495$ | $30771328175$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $31$ | $137$ | $611$ | $3149$ | $15823$ | $78084$ | $389971$ | $1956557$ | $9783651$ |
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 6.0.39563351.1. |
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_bb_ct | $2$ | 3.25.f_f_bx |