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

• Label: 2.47.p_fs
• 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:	$( 1 + 6 x + 47 x^{2} )( 1 + 9 x + 47 x^{2} )$
	$1 + 15 x + 148 x^{2} + 705 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.644169619151$, $\pm0.727918434973$
Angle rank:	$2$ (numerical)
Jacobians:	$18$
Isomorphism classes:	90

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3078$	$5041764$	$10658289096$	$23837177853216$	$52601523316747218$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$63$	$2281$	$102654$	$4884985$	$229355433$	$10778942122$	$506624521599$	$23811287015569$	$1119130430010498$	$52599132445566961$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

• $y^2=37 x^6+46 x^5+3 x^4+4 x^3+14 x^2+22 x+3$
• $y^2=17 x^6+22 x^5+16 x^4+12 x^3+26 x^2+30 x+31$
• $y^2=28 x^6+12 x^5+40 x^4+27 x^3+9 x^2+5 x+14$
• $y^2=27 x^6+45 x^5+27 x^4+24 x^3+41 x^2+15 x+25$
• $y^2=31 x^6+11 x^5+31 x^4+6 x^3+24 x^2+24 x+35$
• $y^2=x^6+46 x^5+23 x^4+42 x^3+39 x^2+36 x+9$
• $y^2=26 x^6+29 x^5+43 x^4+12 x^3+42 x^2+40 x+36$
• $y^2=12 x^6+41 x^5+30 x^4+19 x^3+7 x^2+3 x+30$
• $y^2=35 x^6+39 x^5+36 x^4+4 x^3+15 x^2+30 x+42$
• $y^2=29 x^6+25 x^5+26 x^4+12 x^3+45 x^2+10 x+31$
• $y^2=32 x^6+18 x^5+30 x^4+24 x^3+15 x^2+38 x+39$
• $y^2=16 x^6+20 x^5+36 x^4+30 x^3+18 x^2+12 x+46$
• $y^2=43 x^6+14 x^5+21 x^4+5 x^3+26 x^2+18 x+42$
• $y^2=4 x^6+36 x^4+43 x^3+38 x^2+7 x+25$
• $y^2=17 x^5+15 x^4+16 x^3+28 x^2+42 x+22$
• $y^2=8 x^6+4 x^5+11 x^4+21 x^3+39 x^2+20 x+27$
• $y^2=9 x^6+3 x^5+44 x^4+33 x^3+17 x^2+34 x+9$
• $y^2=8 x^6+5 x^5+40 x^4+46 x^3+31 x^2+x+12$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{47}$

The isogeny class factors as 1.47.g $\times$ 1.47.j and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.47.g : \(\Q(\sqrt{-38}) \).
• 1.47.j : \(\Q(\sqrt{-107}) \).

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.ap_fs	$2$	(not in LMFDB)
2.47.ad_bo	$2$	(not in LMFDB)
2.47.d_bo	$2$	(not in LMFDB)