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

• Label: 1.149.e
• 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:	$1 + 4 x + 149 x^{2}$
Frobenius angles:	$\pm0.552390139656$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-145}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$154$	$22484$	$3306226$	$492849280$	$73440173114$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$154$	$22484$	$3306226$	$492849280$	$73440173114$	$10942530230324$	$1630436387621426$	$242935032501342720$	$36197319891604872154$	$5393400662052389914004$

Jacobians and polarizations

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

• $y^2=x^3+51 x+102$
• $y^2=x^3+43 x+86$
• $y^2=x^3+119 x+119$
• $y^2=x^3+132 x+132$
• $y^2=x^3+143 x+143$
• $y^2=x^3+132 x+115$
• $y^2=x^3+32 x+64$
• $y^2=x^3+45 x+45$

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 \(\Q(\sqrt{-145}) \).

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.ae	$2$	(not in LMFDB)