Properties

 Label 2.83.abd_of 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: $1 - 29 x + 369 x^{2} - 2407 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.107448708646$, $\pm0.275598886837$ Angle rank: $2$ (numerical) Number field: 4.0.5897933.1 Galois group: $D_{4}$ Jacobians: 19

This isogeny class is simple and geometrically 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 19 curves, and hence is principally polarizable:

• $y^2=54x^6+22x^5+74x^4+43x^3+46x^2+41x+15$
• $y^2=42x^6+45x^5+77x^4+68x^3+51x^2+66x+8$
• $y^2=80x^6+56x^5+20x^4+19x^3+40x^2+26x+43$
• $y^2=38x^6+70x^5+34x^4+40x^3+21x^2+41x+70$
• $y^2=32x^6+40x^5+20x^4+74x^3+33x^2+17x+78$
• $y^2=16x^6+77x^5+8x^4+9x^3+24x^2+51x+30$
• $y^2=72x^6+50x^5+38x^4+18x^3+31x^2+45x+18$
• $y^2=14x^6+67x^5+20x^4+81x^3+73x^2+78x+18$
• $y^2=8x^6+55x^5+51x^4+24x^3+52x^2+22x+82$
• $y^2=80x^6+32x^5+74x^4+45x^3+31x^2+44x+81$
• $y^2=19x^6+38x^5+5x^4+63x^3+67x^2+9x+42$
• $y^2=5x^6+6x^5+5x^4+34x^3+39x^2+20x+45$
• $y^2=63x^6+57x^5+52x^4+48x^3+19x^2+75x+62$
• $y^2=38x^6+25x^5+29x^4+75x^3+40x^2+48x+51$
• $y^2=79x^6+42x^5+39x^4+45x^3+81x^2+22x+26$
• $y^2=47x^6+35x^5+23x^4+9x^3+79x^2+40x+21$
• $y^2=52x^6+82x^5+39x^4+71x^3+44x^2+25x+25$
• $y^2=55x^6+6x^5+19x^4+37x^3+66x^2+72x+20$
• $y^2=46x^6+43x^5+65x^4+15x^3+6x^2+76x+52$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4823 46758985 327222372113 2252769576000125 15516283824919307248 106889998411112772513385 736365188812273872199901189 5072820321229502643924105927125 34946659190327794982957837369094587 240747534330018668119344800560745516800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6787 572281 47468379 3939102240 326940344839 27136048244227 2252292242029251 186940256074400473 15516041200543678182

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.5897933.1.
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.bd_of $2$ (not in LMFDB)