Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 9 x + 47 x^{2} - 153 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.162674028495$, $\pm0.429661290527$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.10933.1 |
Galois group: | $D_{4}$ |
Jacobians: | $9$ |
Isomorphism classes: | 9 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $175$ | $87325$ | $24544975$ | $6967225125$ | $2015788054000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $9$ | $303$ | $4995$ | $83419$ | $1419714$ | $24149751$ | $410415903$ | $6975887731$ | $118587324645$ | $2015991105918$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=x^6+8x^5+12x^4+6x^3+16x^2+15x+11$
- $y^2=5x^6+4x^5+2x^4+5x^3+13x^2+x+14$
- $y^2=10x^6+15x^5+13x^4+5x^3+x^2+11x+6$
- $y^2=6x^6+x^5+5x^4+2x^3+11x^2+13x+16$
- $y^2=6x^6+2x^5+15x^4+5x^3+16x^2+15x+14$
- $y^2=3x^6+16x^5+10x^4+2x^3+14x^2+13x+7$
- $y^2=15x^6+3x^5+14x^4+4x^3+9x^2+x+5$
- $y^2=7x^6+7x^5+7x^4+x^3+3x^2+7x+7$
- $y^2=12x^6+11x^5+6x^3+11x^2+13x+12$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{17}$.
Endomorphism algebra over $\F_{17}$The endomorphism algebra of this simple isogeny class is 4.0.10933.1. |
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 |
---|---|---|
2.17.j_bv | $2$ | (not in LMFDB) |