Invariants
Base field: | $\F_{383}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 27 x + 383 x^{2}$ |
Frobenius angles: | $\pm0.257690633423$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-803}) \) |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $357$ | $146727$ | $56193228$ | $21517954731$ | $8241268363167$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $357$ | $146727$ | $56193228$ | $21517954731$ | $8241268363167$ | $3156404410648944$ | $1208902893700863417$ | $463009808932479193203$ | $177332756836862092739364$ | $67918445868695637108870207$ |
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 $\F_{383}$.
Endomorphism algebra over $\F_{383}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-803}) \). |
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 |
---|---|---|
1.383.bb | $2$ | (not in LMFDB) |