Invariants
Base field: | $\F_{19}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4}$ |
Frobenius angles: | $\pm0.0482018232348$, $\pm0.238558256044$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $1$ |
Isomorphism classes: | 1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $155$ | $117025$ | $46735445$ | $16999168525$ | $6131808122000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $5$ | $323$ | $6815$ | $130443$ | $2476400$ | $47040383$ | $893812085$ | $16983221443$ | $322686446195$ | $6131064236198$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=11x^6+8x^5+8x^3+18x^2+2x+18$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{19}$.
Endomorphism algebra over $\F_{19}$The endomorphism algebra of this simple isogeny class is 4.0.1525.1. |
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 |
---|---|---|
2.19.p_dp | $2$ | (not in LMFDB) |