Invariants
Base field: | $\F_{353}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 12 x + 353 x^{2}$ |
Frobenius angles: | $\pm0.396536189938$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-317}) \) |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $342$ | $125172$ | $43997958$ | $15527336256$ | $5481168541542$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $342$ | $125172$ | $43997958$ | $15527336256$ | $5481168541542$ | $1934854113012084$ | $683003514655677942$ | $241100240255502882048$ | $85108384800671968526454$ | $30043259834670495158991732$ |
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 $\F_{353}$.
Endomorphism algebra over $\F_{353}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-317}) \). |
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 |
---|---|---|
1.353.m | $2$ | (not in LMFDB) |