Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 13 x + 84 x^{2} - 299 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.148876346239$, $\pm0.346866314170$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.390728.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $302$ | $279652$ | $150266744$ | $78501672224$ | $41427265132522$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $11$ | $529$ | $12350$ | $280521$ | $6436461$ | $148035322$ | $3404914979$ | $78311872689$ | $1801156445426$ | $41426512933209$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^6+6x^4+14x^3+20x^2+15x+2$
- $y^2=17x^6+12x^5+13x^4+19x^2+8x+14$
- $y^2=5x^6+12x^5+10x^4+15x^3+17x^2+x+2$
- $y^2=10x^6+13x^5+4x^4+12x^3+20x^2+12x+10$
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 4.0.390728.1. |
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.n_dg | $2$ | (not in LMFDB) |