Invariants
| Base field: | $\F_{2^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 3 x + 4 x^{2} )( 1 - 3 x + 6 x^{2} - 12 x^{3} + 16 x^{4} )$ |
| $1 - 6 x + 19 x^{2} - 42 x^{3} + 76 x^{4} - 96 x^{5} + 64 x^{6}$ | |
| Frobenius angles: | $\pm0.150432950460$, $\pm0.230053456163$, $\pm0.544835058382$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $16$ | $4864$ | $270544$ | $17685504$ | $1235306416$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $19$ | $65$ | $271$ | $1169$ | $4351$ | $16337$ | $65279$ | $262577$ | $1047679$ |
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 $\F_{2^{2}}$.
Endomorphism algebra over $\F_{2^{2}}$| The isogeny class factors as 1.4.ad $\times$ 2.4.ad_g 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 |
|---|---|---|
| 3.4.a_b_ag | $2$ | 3.16.c_j_dw |
| 3.4.a_b_g | $2$ | 3.16.c_j_dw |
| 3.4.g_t_bq | $2$ | 3.16.c_j_dw |