Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 15 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$ |
$1 - 29 x + 376 x^{2} - 2407 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.192168636682$, $\pm0.221078141621$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 12 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4830$ | $46860660$ | $327571894440$ | $2253392306272800$ | $15516999503618647650$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6801$ | $572890$ | $47481497$ | $3939283925$ | $326941980354$ | $27136054309055$ | $2252292150101233$ | $186940253832387070$ | $15516041173351970961$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The isogeny class factors as 1.83.ap $\times$ 1.83.ao and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
---|---|---|
2.83.ab_abs | $2$ | (not in LMFDB) |
2.83.b_abs | $2$ | (not in LMFDB) |
2.83.bd_om | $2$ | (not in LMFDB) |