Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 66 x^{2} - 253 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.138214932321$, $\pm0.422974289955$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.593393.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $332$ | $285520$ | $149122448$ | $78192507200$ | $41414403717172$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $13$ | $541$ | $12256$ | $279417$ | $6434463$ | $148059694$ | $3405057361$ | $78311714193$ | $1801152390688$ | $41426506208661$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^5+16x^4+19x^3+6x^2+7x+17$
- $y^2=5x^6+9x^4+18x^3+9x^2+22x+4$
- $y^2=11x^6+13x^5+8x^4+22x^3+9x^2+11x+15$
- $y^2=6x^5+15x^4+9x^3+x^2+4x+22$
- $y^2=21x^5+17x^4+15x^3+21x+15$
- $y^2=7x^6+16x^5+7x^4+17x^3+2x^2+13x+22$
- $y^2=2x^6+18x^5+8x^3+14x^2+6x+5$
- $y^2=7x^6+12x^5+x^4+2x^3+15x^2+7x+12$
- $y^2=5x^6+14x^5+x^4+20x^3+6x^2+4x+1$
- $y^2=20x^6+2x^5+16x^3+15x^2+12x+15$
- $y^2=7x^6+18x^5+10x^4+2x^3+16x^2+21$
- $y^2=3x^6+5x^5+13x^4+10x^3+15x^2+9x+11$
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 4.0.593393.1. |
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_co | $2$ | (not in LMFDB) |