Abelian variety isogeny class 2.127.abl_wl over $\F_{127}$

• Label: 2.127.abl_wl
• Base field: $\F_{127}$
• 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:	$\F_{127}$
Dimension:	$2$
L-polynomial:	$1 - 37 x + 583 x^{2} - 4699 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.0599679824793$, $\pm0.270851269739$
Angle rank:	$2$ (numerical)
Number field:	4.0.14373653.2
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11977$	$256894673$	$4195795467367$	$67677219712425869$	$1091532097710466708912$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$15927$	$2048347$	$260152275$	$33038316276$	$4195869599091$	$532875804928537$	$67675233757465395$	$8594754748198036957$	$1091533853134003648462$

Jacobians and polarizations

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

• $y^2=14 x^6+51 x^5+14 x^4+117 x^3+74 x^2+45 x+114$
• $y^2=122 x^6+42 x^5+67 x^4+102 x^3+30 x^2+51 x+124$
• $y^2=33 x^6+58 x^5+79 x^4+115 x^3+105 x^2+50 x+59$
• $y^2=43 x^6+108 x^5+37 x^4+56 x^3+103 x^2+72 x+43$
• $y^2=107 x^5+69 x^4+47 x^3+20 x^2+66 x+83$
• $y^2=x^6+32 x^5+38 x^4+43 x^3+4 x^2+110$
• $y^2=26 x^6+70 x^5+62 x^4+105 x^3+80 x^2+93 x+70$
• $y^2=46 x^6+78 x^5+65 x^4+52 x^3+110 x^2+74 x+33$
• $y^2=51 x^6+5 x^5+22 x^4+43 x^3+14 x^2+20 x+63$
• $y^2=10 x^6+21 x^5+48 x^4+71 x^3+87 x^2+98 x+72$
• $y^2=106 x^6+37 x^5+59 x^4+31 x^3+77 x^2+3 x+7$
• $y^2=21 x^6+110 x^5+115 x^4+27 x^3+5 x^2+80 x+75$
• $y^2=20 x^6+125 x^5+112 x^4+75 x^3+12 x^2+15 x+36$
• $y^2=81 x^6+11 x^5+54 x^4+85 x^3+74 x^2+54 x+17$
• $y^2=121 x^6+63 x^5+43 x^4+23 x^3+x^2+61 x+74$
• $y^2=113 x^6+116 x^5+50 x^4+35 x^3+81 x^2+73 x+29$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{127}$.

Endomorphism algebra over $\F_{127}$

The endomorphism algebra of this simple isogeny class is 4.0.14373653.2.

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
2.127.bl_wl	$2$	(not in LMFDB)