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

• Label: 1.179.ag
• 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:	$1 - 6 x + 179 x^{2}$
Frobenius angles:	$\pm0.428013141290$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-170}) \)
Galois group:	$C_2$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$174$	$32364$	$5738346$	$1026586080$	$183765221214$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$174$	$32364$	$5738346$	$1026586080$	$183765221214$	$32894115879564$	$5888046460096506$	$1053960289373646720$	$188658891686520800334$	$33769941616049120839404$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):

• $y^2=x^3+125 x+125$
• $y^2=x^3+172 x+165$
• $y^2=x^3+80 x+80$
• $y^2=x^3+111 x+43$
• $y^2=x^3+117 x+55$
• $y^2=x^3+28 x+28$
• $y^2=x^3+83 x+166$
• $y^2=x^3+15 x+30$
• $y^2=x^3+174 x+169$
• $y^2=x^3+97 x+97$
• $y^2=x^3+118 x+118$
• $y^2=x^3+68 x+136$

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 \(\Q(\sqrt{-170}) \).

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.g	$2$	(not in LMFDB)