Abelian variety isogeny class 1.131.u over $\F_{131}$

• Label: 1.131.u
• Base field: $\F_{131}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{131}$
Dimension:	$1$
L-polynomial:	$1 + 20 x + 131 x^{2}$
Frobenius angles:	$\pm0.838288723584$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-31}) \)
Galois group:	$C_2$
Jacobians:	$6$
Isomorphism classes:	6

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:	$1$
Slopes:	$[0, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$152$	$17024$	$2248232$	$294515200$	$38579165752$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$152$	$17024$	$2248232$	$294515200$	$38579165752$	$5053917620864$	$662062574800072$	$86730203824588800$	$11361656653498363352$	$1488377021703863871104$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which 0 are hyperelliptic):

• $y^2=x^3+6 x+12$
• $y^2=x^3+117 x+117$
• $y^2=x^3+93 x+93$
• $y^2=x^3+4 x+4$
• $y^2=x^3+2 x+4$
• $y^2=x^3+45 x+90$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{131}$.

Endomorphism algebra over $\F_{131}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-31}) \).

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
1.131.au	$2$	(not in LMFDB)