Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 65 x^{2} - 253 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.125643553687$, $\pm0.428178140928$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.29725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $6$ |
Isomorphism classes: | 6 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $331$ | $284329$ | $148717969$ | $78130481581$ | $41409806217616$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $13$ | $539$ | $12223$ | $279195$ | $6433748$ | $148058543$ | $3405050585$ | $78311674819$ | $1801152716959$ | $41426511980414$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+2x^5+x^4+17x^3+15x^2+9x+22$
- $y^2=15x^6+20x^5+20x^4+19x^3+3x^2+18x+7$
- $y^2=20x^6+20x^5+15x^4+3x^3+x^2+10x+21$
- $y^2=21x^6+20x^4+18x^3+2x^2+21x+17$
- $y^2=7x^6+22x^5+14x^4+7x^3+5x^2+8x+9$
- $y^2=10x^6+13x^5+2x^4+10x^3+20x^2+14x+17$
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 4.0.29725.1. |
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_cn | $2$ | (not in LMFDB) |