Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 9 x + 53 x^{2} - 153 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.261420712581$, $\pm0.365485551864$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.51525.2 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $181$ | $91405$ | $25356109$ | $7029501525$ | $2015022786256$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $9$ | $315$ | $5157$ | $84163$ | $1419174$ | $24127395$ | $410311197$ | $6975759523$ | $118587992409$ | $2015993569950$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=6x^6+7x^5+2x^4+12x^3+8x^2+10x+6$
- $y^2=15x^6+10x^5+10x^4+15x^3+13x^2+5x+15$
- $y^2=7x^6+6x^5+12x^4+15x^3+2x^2+12x+9$
- $y^2=5x^6+9x^4+5x^3+5x^2+9x+7$
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 4.0.51525.2. |
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 |
---|---|---|
2.17.j_cb | $2$ | (not in LMFDB) |