Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 7 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ |
| $1 - 13 x + 88 x^{2} - 299 x^{3} + 529 x^{4}$ | |
| Frobenius angles: | $\pm0.239612957690$, $\pm0.284877382774$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $306$ | $284580$ | $152200728$ | $78874192800$ | $41460751050246$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $11$ | $537$ | $12506$ | $281849$ | $6441661$ | $148025754$ | $3404647075$ | $78310086481$ | $1801150830518$ | $41426518534257$ |
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 $\times$ 1.23.ag 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 |
|---|---|---|
| 2.23.ab_e | $2$ | (not in LMFDB) |
| 2.23.b_e | $2$ | (not in LMFDB) |
| 2.23.n_dk | $2$ | (not in LMFDB) |