Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4} )$ |
| $1 - 22 x + 223 x^{2} - 1345 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.112386341891$, $\pm0.130958063173$, $\pm0.355407705965$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4515$ | $137820375$ | $1806401347380$ | $21928162286559375$ | $266613459226638913200$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $492$ | $12203$ | $280012$ | $6435817$ | $148045329$ | $3405025192$ | $78312563684$ | $1801159794449$ | $41426528197107$ |
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.aj $\times$ 2.23.an_df 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.ae_al_ft | $2$ | (not in LMFDB) |
| 3.23.e_al_aft | $2$ | (not in LMFDB) |
| 3.23.w_ip_bzt | $2$ | (not in LMFDB) |