Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.144663500024$, $\pm0.268275520367$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.22725.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $271$ | $268561$ | $149694709$ | $78672527901$ | $41463219189136$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $9$ | $507$ | $12303$ | $281131$ | $6442044$ | $148049943$ | $3404833833$ | $78310976323$ | $1801153513179$ | $41426520353022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^5+7x^4+22x^3+6x^2+11x+17$
- $y^2=19x^6+7x^4+8x^3+16x^2+x+5$
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 4.0.22725.1. |
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.p_dx | $2$ | (not in LMFDB) |