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

• Label: 1.131.i
• 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:	$1 + 8 x + 131 x^{2}$
Frobenius angles:	$\pm0.613642289589$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-115}) \)
Galois group:	$C_2$
Jacobians:	$8$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$140$	$17360$	$2245460$	$294495040$	$38579873500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$140$	$17360$	$2245460$	$294495040$	$38579873500$	$5053910713040$	$662062591066660$	$86730204034172160$	$11361656653957764140$	$1488377021661435794000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):

• $y^2=x^3+2 x+2$
• $y^2=x^3+49 x+98$
• $y^2=x^3+41 x+41$
• $y^2=x^3+120 x+109$
• $y^2=x^3+64 x+128$
• $y^2=x^3+49 x+49$
• $y^2=x^3+125 x+119$
• $y^2=x^3+33 x+33$

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 \(\Q(\sqrt{-115}) \).

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.ai	$2$	(not in LMFDB)