Abelian variety isogeny class 2.37.c_cx over $\F_{37}$

• Label: 2.37.c_cx
• Base field: $\F_{37}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{37}$
Dimension:	$2$
L-polynomial:	$( 1 + x + 37 x^{2} )^{2}$
	$1 + 2 x + 75 x^{2} + 74 x^{3} + 1369 x^{4}$
Frobenius angles:	$\pm0.526194466411$, $\pm0.526194466411$
Angle rank:	$1$ (numerical)
Jacobians:	$12$
Cyclic group of points:	no
Non-cyclic primes:	$3, 13$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1521$	$2082249$	$2554695936$	$3502778008041$	$4809508355683161$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$40$	$1516$	$50434$	$1868980$	$69357280$	$2565904822$	$94931205808$	$3512473524004$	$129961770564058$	$4808584561055836$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

• $y^2=10 x^6+6 x^5+26 x^4+7 x^3+7 x^2+30 x+12$
• $y^2=29 x^6+3 x^5+33 x^4+7 x^3+26 x^2+25 x+14$
• $y^2=28 x^6+16 x^5+4 x^4+8 x^3+10 x^2+26 x+12$
• $y^2=9 x^6+16 x^5+17 x^4+10 x^3+9 x^2+35 x+3$
• $y^2=x^6+x^3+27$
• $y^2=26 x^6+7 x^5+5 x^4+35 x^3+20 x^2+x+36$
• $y^2=2 x^6+34 x^5+13 x^4+36 x^3+17 x^2+x+20$
• $y^2=26 x^6+9 x^5+12 x^4+26 x^3+6 x^2+34 x+15$
• $y^2=36 x^6+34 x^5+34 x^4+25 x^3+x^2+12 x+11$
• $y^2=25 x^6+19 x^4+29 x^3+23 x^2+23 x+16$
• $y^2=10 x^6+35 x^5+36 x^4+26 x^3+8 x^2+10 x+20$
• $y^2=36 x^6+3 x^5+24 x^4+7 x^3+20 x^2+36 x+27$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{37}$.

Endomorphism algebra over $\F_{37}$

The isogeny class factors as 1.37.b^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.37.ac_cx	$2$	(not in LMFDB)
2.37.a_cv	$2$	(not in LMFDB)
2.37.aw_hn	$3$	(not in LMFDB)
2.37.ak_cl	$3$	(not in LMFDB)
2.37.ab_abk	$3$	(not in LMFDB)
2.37.l_dg	$3$	(not in LMFDB)
2.37.u_gs	$3$	(not in LMFDB)