Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ |
| $1 - 15 x + 100 x^{2} - 345 x^{3} + 529 x^{4}$ | |
| Frobenius angles: | $\pm0.112386341891$, $\pm0.284877382774$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $4$ |
| Isomorphism classes: | 20 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $270$ | $267300$ | $149133960$ | $78532740000$ | $41440524305850$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $505$ | $12258$ | $280633$ | $6438519$ | $148033690$ | $3404800233$ | $78311158993$ | $1801155879054$ | $41426534571025$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=5x^6+8x^5+13x^4+18x^3+16x^2+11x+20$
- $y^2=7x^6+17x^5+8x^4+14x^3+22x^2+19x+20$
- $y^2=20x^6+15x^5+15x^4+20x^3+21x^2+9x+11$
- $y^2=22x^6+10x^5+4x^4+x^3+4x^2+8x+19$
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 $\times$ 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.ad_ai | $2$ | (not in LMFDB) |
| 2.23.d_ai | $2$ | (not in LMFDB) |
| 2.23.p_dw | $2$ | (not in LMFDB) |