Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 + 2 x + 42 x^{2} + 46 x^{3} + 529 x^{4}$ |
| Frobenius angles: | $\pm0.458865329097$, $\pm0.609541873125$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.184400.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $620$ | $324880$ | $146754620$ | $77997190400$ | $41439136865500$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $26$ | $610$ | $12062$ | $278718$ | $6438306$ | $148041730$ | $3404839142$ | $78311216958$ | $1801150316426$ | $41426502454050$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):
- $y^2=12 x^6+11 x^5+x^4+18 x^3+13 x^2+16 x+21$
- $y^2=13 x^6+2 x^5+10 x^4+7 x^3+5 x^2+18 x+4$
- $y^2=3 x^6+3 x^5+14 x^4+19 x^3+14 x^2+13 x+4$
- $y^2=7 x^5+5 x^4+7 x^3+17 x^2+13 x+10$
- $y^2=3 x^6+10 x^5+5 x^4+x^3+8 x^2+14 x+5$
- $y^2=21 x^6+16 x^5+19 x^3+19 x^2+11 x+22$
- $y^2=16 x^6+14 x^5+8 x^3+13 x^2+x+17$
- $y^2=x^6+6 x^5+21 x^4+18 x^3+20 x^2+14 x$
- $y^2=16 x^6+16 x^5+11 x^4+17 x^3+22 x^2+20 x+6$
- $y^2=x^6+3 x^5+11 x^3+6 x^2+16 x+16$
- $y^2=8 x^6+21 x^4+18 x^3+14 x+16$
- $y^2=6 x^6+19 x^5+21 x^4+22 x^3+22 x^2+16 x+20$
- $y^2=22 x^6+17 x^5+4 x^4+15 x^3+13 x^2+10 x+8$
- $y^2=2 x^6+22 x^5+9 x^4+5 x^3+8 x^2+16 x+2$
- $y^2=16 x^6+5 x^5+6 x^4+21 x^3+11 x^2+21 x+14$
- $y^2=3 x^6+19 x^5+15 x^4+17 x^3+13 x^2+14 x+8$
- $y^2=11 x^6+20 x^5+19 x^4+18 x^3+9 x^2+4 x+12$
- $y^2=16 x^6+8 x^5+21 x^4+4 x^3+17 x^2+13 x$
- $y^2=7 x^6+11 x^5+10 x^4+12 x^3+15 x^2+14 x+11$
- $y^2=6 x^6+10 x^5+11 x^4+2 x^3+18 x^2+21 x+4$
- $y^2=18 x^6+5 x^5+21 x^4+13 x^3+22 x^2+19 x+19$
- $y^2=3 x^6+9 x^4+5 x^3+17 x^2+15 x+10$
- $y^2=7 x^6+8 x^5+4 x^4+21 x^3+x^2+17 x+15$
- $y^2=4 x^6+18 x^5+x^4+10 x^3+19 x^2+6 x+14$
- $y^2=12 x^6+11 x^5+3 x^4+9 x^3+22 x^2+4 x+6$
- $y^2=3 x^6+x^5+x^4+17 x^3+12 x^2+5$
- $y^2=3 x^6+x^5+14 x^4+14 x^3+7 x^2+15 x+15$
- $y^2=15 x^6+16 x^5+18 x^4+2 x^3+8 x^2+4 x+5$
- $y^2=4 x^6+21 x^5+13 x^4+13 x^3+19 x^2+7 x+9$
- $y^2=9 x^6+16 x^5+22 x^4+12 x^3+9 x^2+16 x+13$
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 4.0.184400.1. |
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.ac_bq | $2$ | (not in LMFDB) |