Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 17 x + 136 x^{2} - 671 x^{3} + 2176 x^{4} - 4352 x^{5} + 4096 x^{6}$ |
Frobenius angles: | $\pm0.0601430340549$, $\pm0.180583045112$, $\pm0.403196153073$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.1181001679.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1369$ | $15673681$ | $68892240391$ | $280531131810949$ | $1151500162121819059$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $240$ | $4107$ | $65316$ | $1047285$ | $16779603$ | $268477328$ | $4295081724$ | $68719137186$ | $1099508479275$ |
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 6.0.1181001679.1. |
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_fg_zv | $2$ | (not in LMFDB) |