Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 6 x + 53 x^{2} - 138 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.347772832726$, $\pm0.447131189422$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.415296.4 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $439$ | $319153$ | $152025700$ | $78177484809$ | $41380156752679$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $18$ | $600$ | $12492$ | $279364$ | $6429138$ | $148025670$ | $3404908686$ | $78311284804$ | $1801152448596$ | $41426510955000$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):
- $y^2=14 x^6+15 x^5+12 x^4+11 x^3+14 x^2+2 x+12$
- $y^2=7 x^6+15 x^5+6 x^4+9 x^3+19 x^2+3 x+5$
- $y^2=5 x^6+16 x^5+14 x^4+15 x^3+3 x^2+22 x+4$
- $y^2=4 x^6+12 x^5+9 x^4+3 x^3+21 x^2+13 x+1$
- $y^2=16 x^6+19 x^5+18 x^4+15 x^3+11 x^2+21 x+19$
- $y^2=21 x^6+18 x^5+18 x^4+x^2+2 x+22$
- $y^2=21 x^6+19 x^5+19 x^4+7 x^3+19 x^2+11 x+12$
- $y^2=22 x^6+20 x^5+22 x^4+21 x^3+2 x^2+19 x+11$
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 4.0.415296.4. |
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.g_cb | $2$ | (not in LMFDB) |