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

• Label: 2.127.abn_yi
• Base field: $\F_{127}$
• 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:	$\F_{127}$
Dimension:	$2$
L-polynomial:	$( 1 - 21 x + 127 x^{2} )( 1 - 18 x + 127 x^{2} )$
	$1 - 39 x + 632 x^{2} - 4953 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.118304318667$, $\pm0.205563304889$
Angle rank:	$2$ (numerical)
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11770$	$256044580$	$4195396396840$	$67681646472132000$	$1091549223650441180350$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$89$	$15873$	$2048150$	$260169289$	$33038834639$	$4195878467946$	$532875908567273$	$67675234525787761$	$8594754749127032330$	$1091533853063772839193$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):

• $y^2=24 x^6+41 x^5+78 x^4+47 x^3+12 x^2+29 x+93$
• $y^2=114 x^6+110 x^5+74 x^4+73 x^3+8 x^2+2 x+121$
• $y^2=79 x^6+122 x^5+25 x^4+114 x^3+116 x^2+120 x+9$
• $y^2=11 x^6+13 x^5+13 x^4+77 x^3+37 x^2+88 x+17$
• $y^2=48 x^6+119 x^5+50 x^4+93 x^3+2 x^2+90 x+2$
• $y^2=19 x^6+65 x^5+59 x^4+112 x^3+90 x^2+112 x+28$
• $y^2=67 x^6+88 x^5+103 x^4+126 x^3+80 x^2+73 x+27$
• $y^2=88 x^6+126 x^5+69 x^4+84 x^3+34 x^2+114 x+73$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{127}$

The isogeny class factors as 1.127.av $\times$ 1.127.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.127.av : \(\Q(\sqrt{-67}) \).
• 1.127.as : \(\Q(\sqrt{-46}) \).

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.ad_aeu	$2$	(not in LMFDB)
2.127.d_aeu	$2$	(not in LMFDB)
2.127.bn_yi	$2$	(not in LMFDB)