Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.0613235619868$, $\pm0.259095524151$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.10496.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $254$ | $259588$ | $147834350$ | $78392460944$ | $41427442113454$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $8$ | $490$ | $12152$ | $280134$ | $6436488$ | $148021930$ | $3404702456$ | $78310423614$ | $1801151744456$ | $41426519325450$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+4x^5+4x^4+15x^3+10x^2+20x+22$
- $y^2=7x^6+20x^5+20x^4+8x^3+6x^2+18x+5$
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 4.0.10496.2. |
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.q_ee | $2$ | (not in LMFDB) |