Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 11 x + 67 x^{2} - 253 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.150354367139$, $\pm0.417487041857$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2241053.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $9$ |
| Isomorphism classes: | 9 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $333$ | $286713$ | $149527323$ | $78253439229$ | $41418293691888$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $13$ | $543$ | $12289$ | $279635$ | $6435068$ | $148059459$ | $3405053819$ | $78311704915$ | $1801151914531$ | $41426500091838$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=18x^6+18x^5+14x^4+14x^3+17x^2+15x+17$
- $y^2=5x^6+19x^5+22x^4+19x^3+8x^2+7x+17$
- $y^2=11x^6+17x^4+18x^3+11x^2+7x+20$
- $y^2=x^6+18x^5+19x^4+20x^3+17x^2+3x+14$
- $y^2=15x^6+21x^5+22x^4+2x^3+6x^2+4x+9$
- $y^2=11x^6+13x^5+x^4+15x^3+22x^2+17$
- $y^2=13x^6+10x^5+13x^4+4x^3+16x+1$
- $y^2=15x^6+4x^5+3x^4+13x^3+6x^2+10x+10$
- $y^2=7x^6+22x^5+12x^4+12x^3+14x^2+21x+2$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The endomorphism algebra of this simple isogeny class is 4.0.2241053.1. |
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.l_cp | $2$ | (not in LMFDB) |