# Properties

 Label 2.83.abd_ok 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: $( 1 - 16 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$ Frobenius angles: $\pm0.158801688027$, $\pm0.247123549255$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=66x^6+12x^5+61x^4+x^3+44x^2+14x+70$
• $y^2=39x^6+x^5+22x^4+48x^3+43x^2+63x+62$
• $y^2=26x^6+67x^5+25x^4+69x^3+58x^2+72x+35$
• $y^2=76x^6+57x^5+57x^4+61x^3+71x^2+82x+35$
• $y^2=62x^6+66x^5+48x^4+25x^3+71x^2+6x+5$
• $y^2=14x^6+40x^5+28x^4+18x^3+59x^2+59x+13$
• $y^2=80x^6+23x^5+32x^4+10x^3+57x^2+61x+64$
• $y^2=37x^6+29x^5+40x^4+14x^3+8x^2+18x+47$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4828 46831600 327472019728 2253215327224000 15516800734120996948 106890397780558291513600 736365341951872008618709444 5072820226899067530766745568000 34946658951931111796882619351319312 240747534078666415729767222676943398000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6797 572716 47477769 3939233465 326941566374 27136053887627 2252292200147281 186940254799144468 15516041184344168957

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.aq $\times$ 1.83.an 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.ad_abq $2$ (not in LMFDB) 2.83.d_abq $2$ (not in LMFDB) 2.83.bd_ok $2$ (not in LMFDB)