Abelian variety isogeny class 1.151.au over $\F_{151}$

• Label: 1.151.au
• Base field: $\F_{151}$
• 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:	$\F_{151}$
Dimension:	$1$
L-polynomial:	$1 - 20 x + 151 x^{2}$
Frobenius angles:	$\pm0.197401427848$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-51}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$132$	$22704$	$3444012$	$519921600$	$78503285652$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$132$	$22704$	$3444012$	$519921600$	$78503285652$	$11853917350704$	$1789940680549692$	$270281037871046400$	$40812436747439243172$	$6162677950180235955504$

Jacobians and polarizations

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

• $y^2=x^3+68 x+68$
• $y^2=x^3+20 x+60$
• $y^2=x^3+117 x+117$
• $y^2=x^3+99 x+99$
• $y^2=x^3+51 x+2$
• $y^2=x^3+5 x+15$
• $y^2=x^3+73 x+73$
• $y^2=x^3+55 x+55$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{151}$.

Endomorphism algebra over $\F_{151}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-51}) \).

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
1.151.u	$2$	(not in LMFDB)