Invariants
Base field: | $\F_{433}$ |
Dimension: | $1$ |
L-polynomial: | $1 + 7 x + 433 x^{2}$ |
Frobenius angles: | $\pm0.553795205841$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-187}) \) |
Galois group: | $C_2$ |
Jacobians: | $10$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $441$ | $188307$ | $81173988$ | $35151832611$ | $15220876013721$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $441$ | $188307$ | $81173988$ | $35151832611$ | $15220876013721$ | $6590636872614144$ | $2853745725561485769$ | $1235671900507180829763$ | $535045932927677326560804$ | $231674888957047994315780307$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{433}$.
Endomorphism algebra over $\F_{433}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-187}) \). |
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 |
---|---|---|
1.433.ah | $2$ | (not in LMFDB) |