Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$ |
| $1 - 15 x + 102 x^{2} - 345 x^{3} + 529 x^{4}$ | |
| Frobenius angles: | $\pm0.186011988595$, $\pm0.239612957690$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 2 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $272$ | $269824$ | $150256064$ | $78811273216$ | $41484954325232$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $509$ | $12348$ | $281625$ | $6445419$ | $148063358$ | $3404831733$ | $78310465489$ | $1801148899284$ | $41426495437589$ |
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.ai $\times$ 1.23.ah 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_ak | $2$ | (not in LMFDB) |
| 2.23.b_ak | $2$ | (not in LMFDB) |
| 2.23.p_dy | $2$ | (not in LMFDB) |