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

• Label: 2.127.abo_zc
• 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:	$1 - 40 x + 652 x^{2} - 5080 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.100978501051$, $\pm0.191394081692$
Angle rank:	$2$ (numerical)
Number field:	4.0.10496.2
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11662$	$255421124$	$4193827529374$	$67678956681654416$	$1091545938577012339582$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$15834$	$2047384$	$260158950$	$33038735208$	$4195877912058$	$532875910372264$	$67675234618495614$	$8594754750460300888$	$1091533853075762614714$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which all are hyperelliptic):

• $y^2=114 x^6+122 x^5+98 x^4+70 x^3+84 x^2+13 x+81$
• $y^2=41 x^6+120 x^5+57 x^4+111 x^3+50 x^2+58 x+97$
• $y^2=84 x^6+99 x^5+109 x^4+71 x^3+8 x^2+112 x+48$
• $y^2=85 x^6+37 x^5+76 x^4+38 x^3+119 x^2+61 x+48$
• $y^2=124 x^6+3 x^5+59 x^4+34 x^3+103 x^2+76 x+72$
• $y^2=37 x^6+115 x^5+15 x^4+117 x^3+27 x^2+12 x+17$
• $y^2=8 x^6+124 x^5+24 x^4+69 x^3+112 x^2+48 x+29$
• $y^2=106 x^6+22 x^5+122 x^4+59 x^3+115 x^2+107 x+30$
• $y^2=67 x^6+9 x^5+54 x^4+17 x^3+33 x^2+98 x+88$
• $y^2=65 x^6+116 x^5+102 x^4+70 x^3+x^2+26 x+60$
• $y^2=33 x^6+94 x^5+53 x^4+54 x^3+120 x^2+90 x+28$
• $y^2=27 x^6+88 x^5+82 x^4+117 x^3+70 x^2+92 x+46$
• $y^2=55 x^6+48 x^5+103 x^4+76 x^3+36 x^2+56 x+119$
• $y^2=66 x^6+21 x^5+8 x^4+100 x^3+82 x^2+26 x+120$

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 4.0.10496.2.

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.bo_zc	$2$	(not in LMFDB)