# Properties

 Label 2.83.abg_qf Base Field $\F_{83}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{83}$ Dimension: $2$ L-polynomial: $( 1 - 17 x + 83 x^{2} )( 1 - 15 x + 83 x^{2} )$ Frobenius angles: $\pm0.117184483028$, $\pm0.192168636682$ Angle rank: $2$ (numerical) Jacobians: 9

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 contains the Jacobians of 9 curves, and hence is principally polarizable:

• $y^2=2x^6+33x^5+75x^4+66x^3+4x^2+29x+62$
• $y^2=71x^6+39x^5+16x^4+53x^3+4x^2+18x+5$
• $y^2=24x^6+47x^5+21x^3+76x+6$
• $y^2=45x^6+32x^5+51x^4+30x^3+9x^2+57x+50$
• $y^2=53x^6+49x^5+51x^4+14x^3+x^2+64x+8$
• $y^2=74x^6+40x^5+35x^4+34x^3+39x^2+29x+35$
• $y^2=10x^6+73x^5+9x^4+78x^3+63x^2+8x+27$
• $y^2=44x^6+62x^5+10x^4+68x^3+64x^2+13x+81$
• $y^2=17x^6+42x^5+38x^4+66x^3+63x^2+79x+41$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4623 46225377 326758299984 2252716875293049 15516663756749536623 106890561952325735291136 736365634304534154407843751 5072820483596500624608450520425 34946659092049460912905379232668496 240747534109364510780325257185874751777

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 52 6708 571468 47467268 3939198692 326942068518 27136064661212 2252292314118916 186940255548679924 15516041186322643668

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.ar $\times$ 1.83.ap 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.ac_adl $2$ (not in LMFDB) 2.83.c_adl $2$ (not in LMFDB) 2.83.bg_qf $2$ (not in LMFDB)