Invariants
Base field: | $\F_{83}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 10 x + 83 x^{2}$ |
Frobenius angles: | $\pm0.315076740302$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-58}) \) |
Galois group: | $C_2$ |
Jacobians: | $2$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $74$ | $6956$ | $573278$ | $47467744$ | $3939011194$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $74$ | $6956$ | $573278$ | $47467744$ | $3939011194$ | $326939296844$ | $27136042668718$ | $2252292238281600$ | $186940256019601514$ | $15516041194216632236$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-58}) \). |
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 |
---|---|---|
1.83.k | $2$ | (not in LMFDB) |