Abelian variety isogeny class 1.149.k over $\F_{149}$

• Label: 1.149.k
• Base field: $\F_{149}$
• 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:	$\F_{149}$
Dimension:	$1$
L-polynomial:	$1 + 10 x + 149 x^{2}$
Frobenius angles:	$\pm0.634337290613$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-31}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$160$	$22400$	$3304480$	$492889600$	$73440240800$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$160$	$22400$	$3304480$	$492889600$	$73440240800$	$10942521161600$	$1630436446361120$	$242935033707878400$	$36197319872274017440$	$5393400661994016560000$

Jacobians and polarizations

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

• $y^2=x^3+77 x+5$
• $y^2=x^3+57 x+57$
• $y^2=x^3+36 x+36$
• $y^2=x^3+76 x+3$
• $y^2=x^3+111 x+73$
• $y^2=x^3+59 x+59$
• $y^2=x^3+99 x+49$
• $y^2=x^3+125 x+125$
• $y^2=x^3+7 x+14$
• $y^2=x^3+126 x+126$
• $y^2=x^3+28 x+28$
• $y^2=x^3+117 x+85$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{149}$.

Endomorphism algebra over $\F_{149}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-31}) \).

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
1.149.ak	$2$	(not in LMFDB)