Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 11 x + 63 x^{2} - 187 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.203473685038$, $\pm0.321669352104$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.29525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $3$ |
Isomorphism classes: | 3 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $155$ | $85405$ | $25072955$ | $7046339525$ | $2018243902000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $7$ | $295$ | $5101$ | $84363$ | $1421442$ | $24135535$ | $410319721$ | $6975730323$ | $118587933907$ | $2015993284350$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=7x^6+13x^5+15x^4+14x^3+16x^2+9x+1$
- $y^2=12x^6+15x^5+5x^4+11x^3+6x^2+11x+11$
- $y^2=3x^6+14x^5+10x^4+10x^3+10x^2+11x+5$
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 4.0.29525.1. |
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.l_cl | $2$ | (not in LMFDB) |