Abelian variety isogeny class 1.53.c over $\F_{53}$

• Label: 1.53.c
• Base field: $\F_{53}$
• 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:	$\F_{53}$
Dimension:	$1$
L-polynomial:	$1 + 2 x + 53 x^{2}$
Frobenius angles:	$\pm0.543861900584$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-13}) \)
Galois group:	$C_2$
Jacobians:	$6$
Isomorphism classes:	6
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$56$	$2912$	$148568$	$7885696$	$418221496$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$56$	$2912$	$148568$	$7885696$	$418221496$	$22164562784$	$1174709358424$	$62259683286528$	$3299763700466744$	$174887470525800032$

Jacobians and polarizations

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

• $y^2=x^3+26 x+26$
• $y^2=x^3+47 x+41$
• $y^2=x^3+37 x+21$
• $y^2=x^3+34 x+15$
• $y^2=x^3+49 x+45$
• $y^2=x^3+51 x+51$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{53}$.

Endomorphism algebra over $\F_{53}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-13}) \).

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
1.53.ac	$2$	(not in LMFDB)