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

• Label: 2.83.abf_pn
• 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:	$1 - 31 x + 403 x^{2} - 2573 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.101476209234$, $\pm0.229218298306$
Angle rank:	$2$ (numerical)
Number field:	4.0.795821.3
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4689$	$46407033$	$326923058475$	$2252733493647789$	$15516495934019559504$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$53$	$6735$	$571757$	$47467619$	$3939156088$	$326941193475$	$27136054023691$	$2252292228683059$	$186940255252513991$	$15516041190289736550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=12x^6+68x^5+71x^4+45x^3+59x^2+13x+6$
• $y^2=67x^6+53x^5+46x^4+13x^3+55x^2+15x+63$
• $y^2=57x^6+44x^5+11x^4+18x^3+16x^2+69x+40$
• $y^2=78x^6+62x^5+76x^4+46x^3+2x^2+35x+47$
• $y^2=72x^6+33x^5+5x^4+2x^3+11x^2+14x+13$
• $y^2=48x^6+76x^5+72x^4+64x^3+60x^2+27x+5$
• $y^2=60x^6+53x^5+57x^4+9x^3+26x^2+23x+58$
• $y^2=24x^5+22x^4+65x^3+44x^2+53x+61$
• $y^2=53x^6+21x^5+60x^4+46x^3+6x^2+66x+80$
• $y^2=13x^6+7x^5+68x^4+20x^3+32x^2+12x+54$
• $y^2=20x^6+60x^5+25x^4+21x^3+12x^2+15x+29$
• $y^2=22x^6+33x^5+16x^4+68x^3+74x^2+19x+19$

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 4.0.795821.3.

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.bf_pn	$2$	(not in LMFDB)