Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 17 x + 138 x^{2} - 687 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$ |
Frobenius angles: | $\pm0.0523737408415$, $\pm0.219476755816$, $\pm0.380403485950$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.1426375023.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1387$ | $15949113$ | $69790623547$ | $281625434126637$ | $1151390286952763317$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $244$ | $4161$ | $65572$ | $1047185$ | $16771987$ | $268434432$ | $4294969804$ | $68719031508$ | $1099508355239$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$The endomorphism algebra of this simple isogeny class is 6.0.1426375023.1. |
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 |
---|---|---|
3.16.r_fi_bal | $2$ | (not in LMFDB) |