Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 69 x^{2} - 253 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.174086733330$, $\pm0.405448433343$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1760213.1 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $335$ | $289105$ | $150338285$ | $78372028925$ | $41423951738800$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $13$ | $547$ | $12355$ | $280059$ | $6435948$ | $148054879$ | $3405017629$ | $78311574051$ | $1801150891135$ | $41426489691582$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=20x^6+14x^5+10x^4+4x^3+8x^2+2x+19$
- $y^2=16x^6+2x^5+4x^4+16x^3+4x^2+9x+17$
- $y^2=21x^5+4x^4+15x^3+14x^2+15x+21$
- $y^2=4x^6+14x^5+14x^4+6x^3+5x^2+18x+22$
- $y^2=8x^6+5x^4+17x^3+4x^2+14x+8$
- $y^2=9x^6+12x^5+4x^4+20x^3+18x^2+14x+3$
- $y^2=7x^6+19x^5+4x^4+16x^2+15x+4$
- $y^2=14x^6+12x^5+7x^4+22x^3+3x^2+6x+6$
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 4.0.1760213.1. |
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_cr | $2$ | (not in LMFDB) |