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

• Label: 2.127.abl_wj
• 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:	$1 - 37 x + 581 x^{2} - 4699 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.0346920051049$, $\pm0.275796665246$
Angle rank:	$2$ (numerical)
Number field:	4.0.733037.1
Galois group:	$D_{4}$
Jacobians:	$15$
Isomorphism classes:	15

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11975$	$256827825$	$4195339833725$	$67675581680572125$	$1091528039269590878000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$15923$	$2048125$	$260145979$	$33038193436$	$4195867748591$	$532875781719547$	$67675233491565091$	$8594754745019461825$	$1091533853090705008718$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 15 curves (of which all are hyperelliptic):

• $y^2=11 x^6+15 x^5+44 x^4+116 x^3+95 x^2+69 x+17$
• $y^2=58 x^6+49 x^5+121 x^4+107 x^3+61 x^2+113 x+118$
• $y^2=29 x^6+116 x^5+19 x^4+11 x^3+29 x^2+39$
• $y^2=55 x^6+90 x^5+54 x^4+18 x^3+28 x^2+17 x+106$
• $y^2=43 x^6+5 x^5+33 x^4+86 x^3+53 x^2+35 x+120$
• $y^2=80 x^6+121 x^5+96 x^4+74 x^3+87 x^2+37 x+46$
• $y^2=109 x^6+124 x^5+75 x^4+89 x^3+125 x^2+73 x+6$
• $y^2=68 x^6+51 x^5+12 x^4+41 x^3+113 x^2+98 x+108$
• $y^2=75 x^6+3 x^5+98 x^4+82 x^3+45 x^2+30 x+13$
• $y^2=126 x^6+15 x^5+102 x^4+26 x^3+89 x^2+60 x+55$
• $y^2=67 x^6+22 x^5+49 x^4+86 x^3+112 x^2+25 x+23$
• $y^2=95 x^6+93 x^5+98 x^4+81 x^3+66 x^2+109 x+76$
• $y^2=4 x^6+72 x^5+38 x^4+54 x^2+101 x+87$
• $y^2=28 x^6+27 x^5+44 x^4+113 x^3+7 x^2+39 x+13$
• $y^2=86 x^6+78 x^5+114 x^4+121 x^3+96 x^2+5 x+116$

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 4.0.733037.1.

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
2.127.bl_wj	$2$	(not in LMFDB)