Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 62 x^{2} - 253 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.0820306336664$, $\pm0.442438013535$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.432117.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $328$ | $280768$ | $147506848$ | $77937827584$ | $41391767028088$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $13$ | $533$ | $12124$ | $278505$ | $6430943$ | $148046654$ | $3404963729$ | $78311179825$ | $1801151808436$ | $41426519059613$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+x^5+12x^4+18x^3+21x^2+18x$
- $y^2=20x^6+2x^5+10x^4+20x^3+13x^2+20x+22$
- $y^2=2x^6+6x^5+x^4+11x^3+12x^2+3x+1$
- $y^2=6x^6+18x^5+15x^4+14x^3+3x^2+15x+20$
- $y^2=13x^6+20x^5+19x^4+8x^3+19x^2+8x+19$
- $y^2=8x^5+11x^3+19x^2+7x+21$
- $y^2=11x^6+x^5+12x^4+17x^3+20x^2+4x+5$
- $y^2=21x^6+13x^5+9x^4+5x^3+7x^2+2x+21$
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 4.0.432117.2. |
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.l_ck | $2$ | (not in LMFDB) |