Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 68 x^{2} - 253 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.162255762163$, $\pm0.411666868096$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2029896.1 |
Galois group: | $D_{4}$ |
Jacobians: | $6$ |
Isomorphism classes: | 6 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $334$ | $287908$ | $149932600$ | $78313279264$ | $41421476307754$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $13$ | $545$ | $12322$ | $279849$ | $6435563$ | $148057850$ | $3405040421$ | $78311655409$ | $1801151383726$ | $41426494361225$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=19x^6+9x^5+17x^4+18x^3+15x^2+18x+11$
- $y^2=14x^6+20x^4+5x^3+9x^2+5x+13$
- $y^2=5x^6+4x^5+17x^4+22x^3+6x^2+7x+22$
- $y^2=17x^6+6x^5+17x^4+5x^3+x+21$
- $y^2=10x^6+4x^5+14x^4+2x^3+14x^2+16x+14$
- $y^2=6x^6+22x^5+18x^4+13x^3+11x^2+7x+22$
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 4.0.2029896.1. |
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.l_cq | $2$ | (not in LMFDB) |