Invariants
Base field: | $\F_{131}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 20 x + 131 x^{2}$ |
Frobenius angles: | $\pm0.161711276416$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-31}) \) |
Galois group: | $C_2$ |
Jacobians: | $6$ |
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: | $1$ |
Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $112$ | $17024$ | $2247952$ | $294515200$ | $38579813552$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $112$ | $17024$ | $2247952$ | $294515200$ | $38579813552$ | $5053917620864$ | $662062669001552$ | $86730203824588800$ | $11361656655381271792$ | $1488377021703863871104$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-31}) \). |
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 |
---|---|---|
1.131.u | $2$ | (not in LMFDB) |