Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ |
| $1 - 23 x + 243 x^{2} - 1492 x^{3} + 5589 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.0613235619868$, $\pm0.239612957690$, $\pm0.259095524151$ |
| Angle rank: | $3$ (numerical) |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4318$ | $136802876$ | $1819545179800$ | $22019736747021104$ | $266812073826110743018$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $487$ | $12292$ | $281183$ | $6440611$ | $148026664$ | $3404640765$ | $78309882895$ | $1801149378316$ | $41426515199007$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The isogeny class factors as 1.23.ah $\times$ 2.23.aq_ee 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 |
|---|---|---|
| 3.23.aj_t_u | $2$ | (not in LMFDB) |
| 3.23.j_t_au | $2$ | (not in LMFDB) |
| 3.23.x_jj_cfk | $2$ | (not in LMFDB) |