Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 10 x + 56 x^{2} - 170 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.195976948658$, $\pm0.370295042614$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.187200.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $166$ | $87316$ | $24987814$ | $7016364496$ | $2016346642486$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $8$ | $302$ | $5084$ | $84006$ | $1420108$ | $24138398$ | $410366104$ | $6975887998$ | $118587714488$ | $2015989393022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=6x^6+3x^5+16x^4+13x^3+2x^2+10x+9$
- $y^2=7x^6+10x^5+5x^4+7x^3+12x^2+7x+13$
- $y^2=14x^6+10x^4+14x^3+10x+14$
- $y^2=10x^6+14x^5+3x^4+6x^3+10x^2+2x+7$
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 4.0.187200.1. |
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.k_ce | $2$ | (not in LMFDB) |