Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 57 x^{2} - 176 x^{3} + 256 x^{4} )$ |
| $1 - 18 x + 150 x^{2} - 751 x^{3} + 2400 x^{4} - 4608 x^{5} + 4096 x^{6}$ | |
| Frobenius angles: | $\pm0.0728689886706$, $\pm0.160861246510$, $\pm0.368631800070$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 40 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1270$ | $15270480$ | $68971993120$ | $281276896932000$ | $1151846432542081750$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $233$ | $4112$ | $65489$ | $1047599$ | $16777310$ | $268474919$ | $4295211809$ | $68720093072$ | $1099511147753$ |
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_cf 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_ae_bv | $2$ | (not in LMFDB) |
| 3.16.e_ae_abv | $2$ | (not in LMFDB) |
| 3.16.s_fu_bcx | $2$ | (not in LMFDB) |