Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.147872872551$, $\pm0.436753511906$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.971388.2 |
Galois group: | $D_{4}$ |
Jacobians: | $10$ |
Isomorphism classes: | 10 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $174$ | $86652$ | $24410808$ | $6955729344$ | $2015469561774$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $9$ | $301$ | $4968$ | $83281$ | $1419489$ | $24150418$ | $410418801$ | $6975900769$ | $118587552984$ | $2015992942141$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=11x^6+9x^5+5x^4+16x^3+5x^2+10$
- $y^2=14x^5+11x^4+11x^3+7x^2+14x+7$
- $y^2=12x^6+5x^5+9x^4+12x^3+9x^2+15x+7$
- $y^2=11x^6+2x^5+10x^4+6x^3+6x^2+14x+6$
- $y^2=6x^6+2x^5+14x^4+16x^3+4x^2+2x+7$
- $y^2=14x^6+2x^5+4x^4+14x^3+11x+9$
- $y^2=7x^5+x^4+9x^3+6x^2+7x+1$
- $y^2=2x^6+7x^5+7x^4+10x^3+10x^2+10$
- $y^2=14x^6+16x^5+6x^4+15x^3+13x^2+13x+11$
- $y^2=11x^6+11x^5+2x^4+12x^3+3x^2+4x+14$
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 4.0.971388.2. |
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_bu | $2$ | (not in LMFDB) |