Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.0682102518540$, $\pm0.376537722378$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.357192.2 |
Galois group: | $D_{4}$ |
Jacobians: | $2$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $298$ | $274756$ | $148340824$ | $78112031776$ | $41380432054798$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $11$ | $521$ | $12194$ | $279129$ | $6429181$ | $148012346$ | $3404865475$ | $78311624593$ | $1801154519918$ | $41426508651521$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+10x^5+13x^4+21x^3+3x^2+8x+17$
- $y^2=3x^6+15x^5+16x^4+x^3+19x^2+15$
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 4.0.357192.2. |
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.n_dc | $2$ | (not in LMFDB) |