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

• Label: 2.47.au_hc
• 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:	$1 - 20 x + 184 x^{2} - 940 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.0903824780818$, $\pm0.333813825786$
Angle rank:	$2$ (numerical)
Number field:	4.0.3334400.2
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1434$	$4809636$	$10801990746$	$23812873368336$	$52594568798793114$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$28$	$2178$	$104044$	$4880006$	$229325108$	$10779035202$	$506622998084$	$23811297935998$	$1119130595744188$	$52599132897064578$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=41 x^6+x^5+30 x^4+42 x^3+46 x^2+3 x+22$
• $y^2=23 x^6+15 x^5+5 x^4+17 x^3+2 x^2+3 x+32$
• $y^2=17 x^6+16 x^5+39 x^4+13 x^3+4 x^2+12 x+10$
• $y^2=14 x^6+34 x^5+36 x^4+39 x^3+43 x^2+38 x+6$
• $y^2=38 x^6+18 x^5+11 x^4+27 x^3+34 x^2+13 x+30$
• $y^2=41 x^6+8 x^5+26 x^4+10 x^3+2 x^2+24 x+41$
• $y^2=3 x^6+x^5+42 x^4+23 x^3+41 x^2+x+9$
• $y^2=13 x^6+22 x^5+12 x^4+17 x^3+42 x^2+17 x+41$
• $y^2=34 x^6+45 x^5+12 x^4+24 x^3+3 x^2+37 x+8$
• $y^2=41 x^6+7 x^5+6 x^4+38 x^3+19 x^2+14 x+45$
• $y^2=23 x^6+36 x^5+25 x^4+14 x^3+43 x^2+8 x+12$
• $y^2=10 x^6+37 x^5+15 x^4+27 x^3+43 x^2+22 x+41$
• $y^2=11 x^6+36 x^5+21 x^4+31 x^3+15 x^2+3 x+20$
• $y^2=38 x^6+24 x^5+43 x^4+8 x^3+19 x^2+4 x+35$
• $y^2=19 x^6+6 x^4+25 x^3+24 x^2+25 x+34$
• $y^2=5 x^6+22 x^5+7 x^4+32 x^3+33 x^2+x+39$

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 4.0.3334400.2.

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
2.47.u_hc	$2$	(not in LMFDB)