Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 10 x + 57 x^{2} - 170 x^{3} + 289 x^{4}$ |
Frobenius angles: | $\pm0.216316574334$, $\pm0.356804757520$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.94784.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $167$ | $88009$ | $25138844$ | $7030951001$ | $2016631399207$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $8$ | $304$ | $5114$ | $84180$ | $1420308$ | $24134518$ | $410336564$ | $6975796644$ | $118587739898$ | $2015990823264$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+15x^5+5x^4+11x^3+8x+5$
- $y^2=10x^6+x^5+5x^3+16x^2+4x+12$
- $y^2=10x^6+12x^5+13x^4+11x^3+3x^2+11x+11$
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 4.0.94784.1. |
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_cf | $2$ | (not in LMFDB) |