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

• Label: 2.83.abd_od
• 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:	$1 - 29 x + 367 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0872026692841$, $\pm0.283516371812$
Angle rank:	$2$ (numerical)
Number field:	4.0.6676613.1
Galois group:	$D_{4}$
Jacobians:	$17$
Isomorphism classes:	17

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4821$	$46729953$	$327122528607$	$2252589953882589$	$15516069066930023376$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6783$	$572107$	$47464595$	$3939047720$	$326939781339$	$27136044125357$	$2252292224167795$	$186940256081796517$	$15516041201300929638$

Jacobians and polarizations

This isogeny class contains the Jacobians of 17 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=48x^6+39x^5+73x^4+70x^3+80x^2+13x+58$
• $y^2=23x^6+45x^5+65x^4+77x^3+43x^2+77x+73$
• $y^2=48x^6+59x^5+11x^4+76x^3+60x^2+79x+76$
• $y^2=66x^6+50x^5+76x^4+41x^3+70x^2+71x+57$
• $y^2=6x^6+76x^5+38x^4+18x^3+80x^2+43x+72$
• $y^2=6x^6+51x^5+28x^4+62x^3+20x^2+81x+56$
• $y^2=69x^6+65x^5+33x^4+71x^3+15x^2+18x+76$
• $y^2=66x^6+81x^5+59x^4+71x^3+67x^2+3x+65$
• $y^2=79x^6+68x^5+64x^4+23x^3+23x^2+15x+80$
• $y^2=61x^6+43x^5+47x^4+46x^3+34x^2+60x+80$
• $y^2=18x^5+39x^4+74x^3+9x^2+78x+45$
• $y^2=28x^6+9x^5+62x^4+16x^3+59x^2+40x+24$
• $y^2=14x^6+78x^5+50x^4+73x^3+15x^2+34x+13$
• $y^2=24x^6+60x^5+65x^4+42x^3+79x^2+75x+74$
• $y^2=36x^6+17x^5+43x^4+58x^3+79x^2+65x+48$
• $y^2=14x^6+57x^5+14x^4+79x^3+55x^2+38x+43$
• $y^2=55x^6+24x^5+34x^4+80x^2+79x+16$

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 4.0.6676613.1.

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_od	$2$	(not in LMFDB)