Abelian variety isogeny class 1.311.h over $\F_{311}$

• Label: 1.311.h
• Base field: $\F_{311}$
• 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:	$\F_{311}$
Dimension:	$1$
L-polynomial:	$1 + 7 x + 311 x^{2}$
Frobenius angles:	$\pm0.563596197264$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1195}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$319$	$97295$	$30074044$	$9354816955$	$2909392891229$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$319$	$97295$	$30074044$	$9354816955$	$2909392891229$	$904820318882480$	$281399111325912899$	$87515123947944690195$	$27217203547971971538004$	$8464550303316897760862375$

Jacobians and polarizations

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

• $y^2=x^3+181 x+125$
• $y^2=x^3+217 x+210$
• $y^2=x^3+112 x+112$
• $y^2=x^3+296 x+146$
• $y^2=x^3+286 x+286$
• $y^2=x^3+247 x+247$
• $y^2=x^3+170 x+4$
• $y^2=x^3+187 x+191$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{311}$.

Endomorphism algebra over $\F_{311}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1195}) \).

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
1.311.ah	$2$	(not in LMFDB)