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

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

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 29 x + 366 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0761778611858$, $\pm0.287099181260$
Angle rank:	$2$ (numerical)
Number field:	4.0.1601993.1
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4820$	$46715440$	$327072610160$	$2252499859582400$	$15515959974845775100$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6781$	$572020$	$47462697$	$3939020025$	$326939483494$	$27136041662155$	$2252292207567633$	$186940255968937420$	$15516041200218630861$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=3x^6+69x^4+42x^3+78x^2+47x+60$
• $y^2=72x^6+29x^5+68x^4+39x^3+35x^2+61x+28$
• $y^2=74x^6+81x^5+71x^4+70x^3+48x^2+5x+2$
• $y^2=27x^6+82x^5+7x^4+82x^3+46x^2+71x+25$
• $y^2=3x^6+64x^5+30x^4+36x^3+55x^2+31x+3$
• $y^2=52x^6+70x^5+21x^4+51x^3+49x^2+5x+33$
• $y^2=24x^6+29x^5+9x^4+76x^3+70x^2+54x+76$
• $y^2=60x^6+43x^5+5x^4+x^3+61x^2+59x+39$
• $y^2=13x^6+55x^5+22x^4+52x^3+45x^2+9x+67$
• $y^2=15x^6+2x^5+32x^4+9x^3+67x^2+7x+22$
• $y^2=13x^6+27x^5+13x^4+63x^3+54x^2+34x+6$
• $y^2=62x^6+56x^5+22x^4+31x^3+18x^2+59x+82$
• $y^2=53x^6+33x^5+4x^4+72x^3+37x+43$
• $y^2=34x^6+53x^5+40x^4+45x^3+49x^2+20x+10$
• $y^2=2x^6+2x^5+56x^4+14x^3+49x^2+49x+50$
• $y^2=73x^6+66x^5+25x^4+32x^3+15x^2+30x+66$
• $y^2=52x^6+70x^5+x^4+10x^3+52x^2+79x+73$
• $y^2=11x^6+79x^5+52x^4+56x^3+38x^2+65x+73$
• $y^2=49x^6+15x^5+16x^4+57x^3+42x^2+67x+5$
• $y^2=78x^6+29x^5+33x^4+47x^3+29x^2+71x+31$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is 4.0.1601993.1.

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_oc	$2$	(not in LMFDB)