Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 7 x + 25 x^{2} - 56 x^{3} + 64 x^{4} )$ |
| $1 - 12 x + 68 x^{2} - 237 x^{3} + 544 x^{4} - 768 x^{5} + 512 x^{6}$ | |
| Frobenius angles: | $\pm0.113218980851$, $\pm0.154919815756$, $\pm0.403003401001$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 3 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $108$ | $231336$ | $136940544$ | $68492574864$ | $35171229540348$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $57$ | $522$ | $4081$ | $32757$ | $263430$ | $2104701$ | $16797281$ | $134239410$ | $1073726457$ |
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 $\F_{2^{3}}$.
Endomorphism algebra over $\F_{2^{3}}$| The isogeny class factors as 1.8.af $\times$ 2.8.ah_z 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 |
|---|---|---|
| 3.8.ac_ac_n | $2$ | (not in LMFDB) |
| 3.8.c_ac_an | $2$ | (not in LMFDB) |
| 3.8.m_cq_jd | $2$ | (not in LMFDB) |