Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 17 x + 134 x^{2} - 655 x^{3} + 2144 x^{4} - 4352 x^{5} + 4096 x^{6}$ |
Frobenius angles: | $\pm0.0752779416406$, $\pm0.138403566317$, $\pm0.420922033917$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.158451551.1 |
Galois group: | $S_4\times C_2$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1351$ | $15400049$ | $67998430675$ | $279372612310029$ | $1151216629470707121$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $236$ | $4053$ | $65044$ | $1047025$ | $16783691$ | $268503144$ | $4295185420$ | $68719717416$ | $1099512210591$ |
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 6.0.158451551.1. |
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_fe_zf | $2$ | (not in LMFDB) |