Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.166921904620$, $\pm0.337099187115$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.272597.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $7$ |
| Isomorphism classes: | 7 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $303$ | $280881$ | $150749469$ | $78596402301$ | $41436887174448$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $11$ | $531$ | $12389$ | $280859$ | $6437956$ | $148035951$ | $3404876395$ | $78311586403$ | $1801155311033$ | $41426509763646$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^6+7x^5+12x^3+19x^2+9x+17$
- $y^2=14x^6+4x^5+x^4+18x^3+14x^2+21x+11$
- $y^2=11x^6+18x^5+10x^4+8x^3+2x^2+21x+20$
- $y^2=10x^6+14x^5+14x^4+18x^3+15x^2+6x+21$
- $y^2=11x^6+12x^5+x^4+9x^3+7x^2+2x+21$
- $y^2=10x^6+8x^5+14x^4+18x^3+9x^2+21x+6$
- $y^2=10x^6+15x^5+3x^4+10x^3+5x^2+x+9$
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 4.0.272597.1. |
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.n_dh | $2$ | (not in LMFDB) |