Abelian variety isogeny class 1.179.u over $\F_{179}$

• Label: 1.179.u
• Base field: $\F_{179}$
• 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:	$\F_{179}$
Dimension:	$1$
L-polynomial:	$1 + 20 x + 179 x^{2}$
Frobenius angles:	$\pm0.768714908378$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-79}) \)
Galois group:	$C_2$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$200$	$32000$	$5732600$	$1026688000$	$183765241000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$200$	$32000$	$5732600$	$1026688000$	$183765241000$	$32894117408000$	$5888046362685400$	$1053960287058432000$	$188658891737653425800$	$33769941616079424800000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which 0 are hyperelliptic):

• $y^2=x^3+164 x+149$
• $y^2=x^3+83 x+83$
• $y^2=x^3+147 x+115$
• $y^2=x^3+42 x+42$
• $y^2=x^3+129 x+79$
• $y^2=x^3+103 x+27$
• $y^2=x^3+36 x+72$
• $y^2=x^3+60 x+60$
• $y^2=x^3+121 x+63$
• $y^2=x^3+59 x+118$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{179}$.

Endomorphism algebra over $\F_{179}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-79}) \).

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
1.179.au	$2$	(not in LMFDB)