Properties

 Label 2.83.abd_om Base Field $\F_{83}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

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Invariants

 Base field: $\F_{83}$ Dimension: $2$ L-polynomial: $( 1 - 15 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$ Frobenius angles: $\pm0.192168636682$, $\pm0.221078141621$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4830 46860660 327571894440 2253392306272800 15516999503618647650 106890533127865261494720 736365353387823535959324210 5072820114180749092758121680000 34946658771205237652076823773877320 240747533908111018931853372230984253300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6801 572890 47481497 3939283925 326941980354 27136054309055 2252292150101233 186940253832387070 15516041173351970961

Decomposition and endomorphism algebra

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:
All geometric endomorphisms are defined over $\F_{83}$.

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)