Abelian variety isogeny class 1.97.c over $\F_{97}$

• Label: 1.97.c
• Base field: $\F_{97}$
• 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:	$\F_{97}$
Dimension:	$1$
L-polynomial:	$1 + 2 x + 97 x^{2}$
Frobenius angles:	$\pm0.532375263179$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-6}) \)
Galois group:	$C_2$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$100$	$9600$	$912100$	$88512000$	$8587430500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$100$	$9600$	$912100$	$88512000$	$8587430500$	$832973500800$	$80798272732900$	$7837433472768000$	$760231060037068900$	$73742412698523888000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which 0 are hyperelliptic):

• $y^2=x^3+43 x+21$
• $y^2=x^3+65 x+65$
• $y^2=x^3+44 x+44$
• $y^2=x^3+42 x+16$
• $y^2=x^3+62 x+19$
• $y^2=x^3+51 x+51$
• $y^2=x^3+30 x+30$
• $y^2=x^3+75 x+84$
• $y^2=x^3+92 x+92$
• $y^2=x^3+79 x+79$
• $y^2=x^3+36 x+83$
• $y^2=x^3+27 x+38$
• $y^2=x^3+35 x+35$
• $y^2=x^3+30 x+53$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-6}) \).

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
1.97.ac	$2$	(not in LMFDB)