Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 13 x + 81 x^{2} - 299 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.0921437596788$, $\pm0.370068381004$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.488621.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $299$ | $275977$ | $148821569$ | $78211053869$ | $41393392612624$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $11$ | $523$ | $12233$ | $279483$ | $6431196$ | $148021183$ | $3404909519$ | $78311920131$ | $1801156330649$ | $41426516107518$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=19x^6+18x^5+3x^4+8x^3+12x^2+19x+5$
- $y^2=9x^5+4x^4+x^3+13x^2+2x+5$
- $y^2=21x^6+12x^5+x^4+8x^3+9x^2+6$
- $y^2=20x^6+19x^4+15x^3+17x^2+6x+15$
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 4.0.488621.1. |
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_dd | $2$ | (not in LMFDB) |