Invariants
Base field: | $\F_{71}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 10 x + 71 x^{2}$ |
Frobenius angles: | $\pm0.297788873486$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-46}) \) |
Galois group: | $C_2$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $62$ | $5084$ | $359042$ | $25420000$ | $1804232302$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $62$ | $5084$ | $359042$ | $25420000$ | $1804232302$ | $128099722844$ | $9095114338162$ | $645753512880000$ | $45848500948027742$ | $3255243554609637404$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{71}$.
Endomorphism algebra over $\F_{71}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-46}) \). |
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 |
---|---|---|
1.71.k | $2$ | (not in LMFDB) |