Invariants
| Base field: | $\F_{163}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 23 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$ |
| $1 - 45 x + 832 x^{2} - 7335 x^{3} + 26569 x^{4}$ | |
| Frobenius angles: | $\pm0.143017980409$, $\pm0.169471200781$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $20022$ | $696405204$ | $18751870232424$ | $498339725245423776$ | $13239754048664089849482$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $119$ | $26209$ | $4329938$ | $705951865$ | $115064643269$ | $18755386042498$ | $3057125443974623$ | $498311416205692849$ | $81224760543600100934$ | $13239635966936079926689$ |
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 $\F_{163}$.
Endomorphism algebra over $\F_{163}$| The isogeny class factors as 1.163.ax $\times$ 1.163.aw 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 |
|---|---|---|
| 2.163.ab_agy | $2$ | (not in LMFDB) |
| 2.163.b_agy | $2$ | (not in LMFDB) |
| 2.163.bt_bga | $2$ | (not in LMFDB) |