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

• Label: 2.83.abe_or
• 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:	$1 - 30 x + 381 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0255332992515$, $\pm0.274903135578$
Angle rank:	$2$ (numerical)
Number field:	4.0.654400.2
Galois group:	$D_{4}$
Jacobians:	$2$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4751$	$46517041$	$326836702244$	$2252293769242921$	$15515775895125056711$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$6752$	$571608$	$47458356$	$3938973294$	$326938842398$	$27136032045498$	$2252292079179748$	$186940254548328984$	$15516041187282984272$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=52x^6+18x^5+43x^4+37x^3+33x^2+56x+72$
• $y^2=31x^6+69x^5+37x^4+56x^3+39x^2+47x+58$

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 4.0.654400.2.

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.be_or	$2$	(not in LMFDB)