Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 + 14 x + 93 x^{2} + 322 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.697869989030$, $\pm0.840619359759$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.82496.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $5$ |
| Isomorphism classes: | 5 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $959$ | $275233$ | $145672100$ | $78670674089$ | $41401383034879$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $38$ | $520$ | $11972$ | $281124$ | $6432438$ | $148039750$ | $3404825546$ | $78311204484$ | $1801150406876$ | $41426520318600$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which all are hyperelliptic):
- $y^2=x^6+14 x^5+13 x^4+22 x^3+6 x^2+10 x+19$
- $y^2=12 x^6+4 x^5+x^4+10 x^3+21 x^2+20 x+4$
- $y^2=12 x^6+17 x^5+5 x^4+3 x^3+12 x^2+6 x+18$
- $y^2=8 x^6+10 x^5+10 x^4+16 x^3+6 x^2+12 x+9$
- $y^2=12 x^6+x^5+15 x^4+5 x^3+6 x^2+8$
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 4.0.82496.2. |
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.ao_dp | $2$ | (not in LMFDB) |