Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$ |
| $1 - 13 x + 86 x^{2} - 299 x^{3} + 529 x^{4}$ | |
| Frobenius angles: | $\pm0.186011988595$, $\pm0.325452467839$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $4$ |
| Isomorphism classes: | 10 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $304$ | $282112$ | $151232704$ | $78690064384$ | $41445675302224$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $11$ | $533$ | $12428$ | $281193$ | $6439321$ | $148034558$ | $3404818519$ | $78311185201$ | $1801153883204$ | $41426508536093$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=22x^6+8x^5+x^4+18x^3+19x^2+18x+17$
- $y^2=20x^6+21x^5+19x^4+12x^3+6x^2+20x+6$
- $y^2=20x^6+8x^5+11x^4+3x^3+10x^2+16x$
- $y^2=13x^6+5x^5+2x^4+17x^3+3x^2+3x+21$
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.af 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_g | $2$ | (not in LMFDB) |
| 2.23.d_g | $2$ | (not in LMFDB) |
| 2.23.n_di | $2$ | (not in LMFDB) |