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

• Label: 1.97.ah
• 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:	$1 - 7 x + 97 x^{2}$
Frobenius angles:	$\pm0.384354480591$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-339}) \)
Galois group:	$C_2$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$91$	$9555$	$914368$	$88527075$	$8587160491$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$9555$	$914368$	$88527075$	$8587160491$	$832970960640$	$80798294605483$	$7837433766564675$	$760231058877524416$	$73742412674351332275$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which 0 are hyperelliptic):

• $y^2=x^3+67 x+44$
• $y^2=x^3+16 x+16$
• $y^2=x^3+12 x+12$
• $y^2=x^3+94 x+82$
• $y^2=x^3+55 x+55$
• $y^2=x^3+13 x+65$

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 \(\Q(\sqrt{-339}) \).

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.h	$2$	(not in LMFDB)