Abelian variety isogeny class 1.127.m over $\F_{127}$

• Label: 1.127.m
• Base field: $\F_{127}$
• 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:	$\F_{127}$
Dimension:	$1$
L-polynomial:	$1 + 12 x + 127 x^{2}$
Frobenius angles:	$\pm0.678714990332$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-91}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$140$	$16240$	$2045540$	$260164800$	$33038488700$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$140$	$16240$	$2045540$	$260164800$	$33038488700$	$4195868923120$	$532875892914260$	$67675234354963200$	$8594754743082974060$	$1091533853125239689200$

Jacobians and polarizations

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

• $y^2=x^3+121 x+121$
• $y^2=x^3+67 x+74$
• $y^2=x^3+124 x+118$
• $y^2=x^3+55 x+38$
• $y^2=x^3+5 x+5$
• $y^2=x^3+32 x+96$
• $y^2=x^3+92 x+22$
• $y^2=x^3+56 x+56$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{127}$.

Endomorphism algebra over $\F_{127}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-91}) \).

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
1.127.am	$2$	(not in LMFDB)