Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 79 x^{2} - 299 x^{3} + 529 x^{4} )$ |
| $1 - 22 x + 219 x^{2} - 1309 x^{3} + 5037 x^{4} - 11638 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.0326071920932$, $\pm0.112386341891$, $\pm0.382576753817$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4455$ | $135400815$ | $1783198341540$ | $21817987023088575$ | $266290481393365532400$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $484$ | $12047$ | $278604$ | $6428017$ | $148014097$ | $3404890876$ | $78311684612$ | $1801154198417$ | $41426505443059$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains 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_db 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_ap_ej | $2$ | (not in LMFDB) |
| 3.23.e_ap_aej | $2$ | (not in LMFDB) |
| 3.23.w_il_byj | $2$ | (not in LMFDB) |