Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 16 x^{2} )( 1 - 12 x + 65 x^{2} - 192 x^{3} + 256 x^{4} )$ |
| $1 - 19 x + 165 x^{2} - 839 x^{3} + 2640 x^{4} - 4864 x^{5} + 4096 x^{6}$ | |
| Frobenius angles: | $\pm0.0826163580681$, $\pm0.160861246510$, $\pm0.320878822416$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 32 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1180$ | $14896320$ | $69208190620$ | $282707366123520$ | $1153429935459389500$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $226$ | $4126$ | $65822$ | $1049038$ | $16777282$ | $268450222$ | $4295139518$ | $68720417662$ | $1099514380066$ |
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.am_cn 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.af_ad_ct | $2$ | (not in LMFDB) |
| 3.16.f_ad_act | $2$ | (not in LMFDB) |
| 3.16.t_gj_bgh | $2$ | (not in LMFDB) |