Invariants
Base field: | $\F_{449}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 12 x + 449 x^{2}$ |
Frobenius angles: | $\pm0.408618081450$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-413}) \) |
Galois group: | $C_2$ |
Jacobians: | $20$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $438$ | $202356$ | $90533286$ | $40642797888$ | $18248682011718$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $438$ | $202356$ | $90533286$ | $40642797888$ | $18248682011718$ | $8193661996924404$ | $3678954252376574742$ | $1651850457811797374208$ | $741680855532358479315414$ | $333014704134403167535519476$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{449}$.
Endomorphism algebra over $\F_{449}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-413}) \). |
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 |
---|---|---|
1.449.m | $2$ | (not in LMFDB) |