Abelian variety isogeny class 2.83.abe_os over $\F_{83}$

• Label: 2.83.abe_os
• Base field: $\F_{83}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$( 1 - 18 x + 83 x^{2} )( 1 - 12 x + 83 x^{2} )$
	$1 - 30 x + 382 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0496118990883$, $\pm0.271155063531$
Angle rank:	$2$ (numerical)
Jacobians:	$30$
Isomorphism classes:	200

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4752$	$46531584$	$326888355024$	$2252392220491776$	$15515905884131066832$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$6754$	$571698$	$47460430$	$3939006294$	$326939250418$	$27136036291698$	$2252292120115294$	$186940254961923894$	$15516041191968600514$

Jacobians and polarizations

This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=82x^6+49x^5+63x^4+23x^3+63x^2+49x+82$
• $y^2=82x^6+11x^5+20x^4+55x^3+25x^2+22x+34$
• $y^2=18x^6+82x^5+57x^4+79x^3+57x^2+82x+18$
• $y^2=46x^6+29x^5+33x^4+79x^3+40x^2+75x+5$
• $y^2=51x^6+49x^5+44x^4+65x^3+78x^2+54x+73$
• $y^2=27x^6+20x^5+9x^4+48x^3+79x^2+33x+46$
• $y^2=39x^6+13x^5+72x^4+42x^3+72x^2+13x+39$
• $y^2=69x^6+21x^5+69x^4+36x^3+58x^2+24x+74$
• $y^2=73x^6+46x^5+63x^4+15x^3+58x^2+81x+35$
• $y^2=70x^6+19x^5+5x^4+16x^3+39x^2+67x+12$
• $y^2=36x^6+67x^5+66x^4+62x^3+65x^2+8x+28$
• $y^2=36x^6+24x^5+18x^4+12x^3+48x^2+36x+11$
• $y^2=5x^6+49x^5+36x^4+57x^3+36x^2+49x+5$
• $y^2=73x^6+38x^5+51x^4+20x^3+53x^2+11x+82$
• $y^2=16x^6+79x^5+56x^4+4x^3+74x^2+18x+59$
• $y^2=24x^6+54x^5+62x^4+57x^3+59x^2+55x+57$
• $y^2=19x^6+28x^5+2x^4+8x^3+9x^2+58x+60$
• $y^2=13x^6+82x^5+61x^4+40x^3+65x^2+35x+5$
• $y^2=40x^6+74x^5+44x^4+81x^3+3x^2+80x+16$
• $y^2=60x^6+x^5+5x^4+65x^3+38x^2+18x+13$
• $y^2=29x^6+27x^5+51x^4+59x^3+43x^2+35x+31$
• $y^2=28x^6+39x^5+6x^4+20x^3+10x^2+8x+67$
• $y^2=79x^6+58x^5+29x^4+72x^3+29x^2+58x+79$
• $y^2=55x^6+54x^5+39x^4+82x^3+75x^2+76x+34$
• $y^2=18x^6+56x^5+64x^4+80x^3+24x^2+41x+42$
• $y^2=39x^6+59x^5+29x^4+46x^3+36x^2+18x+74$
• $y^2=35x^6+12x^5+77x^4+73x^3+28x^2+49x+62$
• $y^2=79x^6+37x^5+4x^4+45x^3+76x^2+74x+22$
• $y^2=78x^6+30x^5+9x^4+9x^3+15x^2+79x+52$
• $y^2=67x^6+10x^5+79x^4+44x^3+28x^2+51x+24$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.as $\times$ 1.83.am and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.83.as : \(\Q(\sqrt{-2}) \).
• 1.83.am : \(\Q(\sqrt{-47}) \).

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.ag_aby	$2$	(not in LMFDB)
2.83.g_aby	$2$	(not in LMFDB)
2.83.be_os	$2$	(not in LMFDB)