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

• Label: 2.47.aw_ih
• Base field: $\F_{47}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{47}$
Dimension:	$2$
L-polynomial:	$( 1 - 11 x + 47 x^{2} )^{2}$
	$1 - 22 x + 215 x^{2} - 1034 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.203632126579$, $\pm0.203632126579$
Angle rank:	$1$ (numerical)
Jacobians:	$3$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1369$	$4765489$	$10825153936$	$23847312323641$	$52613003936311009$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$26$	$2156$	$104264$	$4887060$	$229405486$	$10779533822$	$506623781410$	$23811278963044$	$1119130357352408$	$52599131324415836$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which all are hyperelliptic):

• $y^2=5 x^6+31 x^5+32 x^4+7 x^3+32 x^2+31 x+5$
• $y^2=15 x^6+25 x^5+x^4+21 x^3+23 x^2+x+23$
• $y^2=26 x^6+4 x^5+39 x^4+21 x^3+37 x^2+13 x+38$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{47}$

The isogeny class factors as 1.47.al^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.47.a_abb	$2$	(not in LMFDB)
2.47.w_ih	$2$	(not in LMFDB)
2.47.l_cw	$3$	(not in LMFDB)