Invariants
Base field: | $\F_{3^{2}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 12 x + 71 x^{2} - 263 x^{3} + 639 x^{4} - 972 x^{5} + 729 x^{6}$ |
Frobenius angles: | $\pm0.0686978556945$, $\pm0.249138957169$, $\pm0.398269757982$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.50290919.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $193$ | $518591$ | $408369472$ | $282860793631$ | $204613810823888$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $80$ | $769$ | $6572$ | $58683$ | $530573$ | $4783112$ | $43046580$ | $387395959$ | $3486728735$ |
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 $\F_{3^{2}}$.
Endomorphism algebra over $\F_{3^{2}}$The endomorphism algebra of this simple isogeny class is 6.0.50290919.1. |
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 |
---|---|---|
3.9.m_ct_kd | $2$ | (not in LMFDB) |