Abelian variety isogeny class 2.47.at_gl over $\F_{47}$

• Label: 2.47.at_gl
• Base field: $\F_{47}$
• 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:	$\F_{47}$
Dimension:	$2$
L-polynomial:	$1 - 19 x + 167 x^{2} - 893 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.0292875227883$, $\pm0.372493218920$
Angle rank:	$2$ (numerical)
Number field:	4.0.1204533.1
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1465$	$4818385$	$10777077655$	$23791860074125$	$52586601112361200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$29$	$2183$	$103805$	$4875699$	$229290364$	$10778884931$	$506622453583$	$23811289169011$	$1119130457771915$	$52599131660159918$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which all are hyperelliptic):

• $y^2=26 x^6+21 x^5+21 x^4+17 x^3+33 x^2+10 x$
• $y^2=46 x^6+10 x^5+31 x^4+20 x^3+7 x^2+14 x+41$
• $y^2=35 x^6+39 x^5+x^4+7 x^3+32 x^2+43 x+5$
• $y^2=30 x^6+32 x^5+24 x^4+6 x^3+29 x^2+23 x+38$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{47}$.

Endomorphism algebra over $\F_{47}$

The endomorphism algebra of this simple isogeny class is 4.0.1204533.1.

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
2.47.t_gl	$2$	(not in LMFDB)