Abelian variety isogeny class 1.157.d over $\F_{157}$

• Label: 1.157.d
• Base field: $\F_{157}$
• 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:	$\F_{157}$
Dimension:	$1$
L-polynomial:	$1 + 3 x + 157 x^{2}$
Frobenius angles:	$\pm0.538197450972$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-619}) \)
Galois group:	$C_2$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$161$	$24955$	$3868508$	$607529475$	$95389341341$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$24955$	$3868508$	$607529475$	$95389341341$	$14976077650240$	$2351243205322193$	$369145193876482275$	$57955795561450179596$	$9099059901108529802275$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which 0 are hyperelliptic):

• $y^2=x^3+139 x+121$
• $y^2=x^3+140 x+123$
• $y^2=x^3+29 x+29$
• $y^2=x^3+88 x+19$
• $y^2=x^3+124 x+124$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-619}) \).

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
1.157.ad	$2$	(not in LMFDB)