Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 18 x + 152 x^{2} - 767 x^{3} + 2432 x^{4} - 4608 x^{5} + 4096 x^{6}$ |
Frobenius angles: | $\pm0.0594651251591$, $\pm0.214320821692$, $\pm0.338587853715$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.140908967.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 20 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1288$ | $15551312$ | $69975592288$ | $282817808471072$ | $1152494692905722488$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $237$ | $4172$ | $65849$ | $1048189$ | $16770606$ | $268413907$ | $4294955409$ | $68719541828$ | $1099511089637$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$The endomorphism algebra of this simple isogeny class is 6.0.140908967.1. |
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.s_fw_bdn | $2$ | (not in LMFDB) |