Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4} )$ |
$1 - 18 x + 152 x^{2} - 765 x^{3} + 2432 x^{4} - 4608 x^{5} + 4096 x^{6}$ | |
Frobenius angles: | $\pm0.133878927982$, $\pm0.160861246510$, $\pm0.347077071791$ |
Angle rank: | $3$ (numerical) |
Isomorphism classes: | 8 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1290$ | $15572880$ | $70106706360$ | $283450491672480$ | $1154387250938439750$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $237$ | $4178$ | $65993$ | $1049909$ | $16784118$ | $268490627$ | $4295276561$ | $68720466962$ | $1099512135597$ |
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 isogeny class factors as 1.16.ah $\times$ 2.16.al_ch and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ae_ac_cj | $2$ | (not in LMFDB) |
3.16.e_ac_acj | $2$ | (not in LMFDB) |
3.16.s_fw_bdl | $2$ | (not in LMFDB) |