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

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

Invariants

Base field:	$\F_{37}$
Dimension:	$2$
L-polynomial:	$1 - 18 x + 150 x^{2} - 666 x^{3} + 1369 x^{4}$
Frobenius angles:	$\pm0.125233054605$, $\pm0.312338589828$
Angle rank:	$2$ (numerical)
Number field:	4.0.55600.1
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	24

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:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$836$	$1842544$	$2579428676$	$3516134085376$	$4808807916713636$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$20$	$1346$	$50924$	$1876110$	$69347180$	$2565704882$	$94931934068$	$3512483186974$	$129961779701348$	$4808584598162786$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=12x^6+13x^5+3x^4+14x^3+4x^2+26x+25$
• $y^2=15x^6+8x^5+24x^4+27x^3+9x^2+23x+28$
• $y^2=21x^6+30x^5+5x^4+35x^3+11x^2+36x+5$
• $y^2=18x^6+31x^5+24x^4+26x^3+13x^2+19x+34$
• $y^2=5x^6+10x^5+22x^4+11x^3+8x^2+13x+23$
• $y^2=4x^6+24x^5+16x^4+21x^3+7x^2+24x+7$
• $y^2=31x^6+12x^5+27x^4+5x^3+22x^2+32x+6$
• $y^2=20x^6+23x^5+31x^4+13x^3+15x^2+8x+1$
• $y^2=19x^6+27x^5+16x^4+31x^3+27x^2+10x+35$
• $y^2=28x^6+8x^4+6x^3+6x^2+14x+32$
• $y^2=14x^6+25x^5+7x^4+28x^3+21x^2+22x+31$
• $y^2=11x^6+24x^5+7x^4+34x^3+10x+27$
• $y^2=4x^6+8x^5+8x^4+11x^3+30x^2+8x+4$
• $y^2=32x^6+26x^5+18x^4+14x^3+12x^2+11x+22$
• $y^2=2x^6+22x^5+9x^4+26x^3+25x^2+6x+14$
• $y^2=17x^6+22x^5+21x^4+31x^3+31x^2+14x+5$
• $y^2=29x^6+x^5+14x^4+24x^3+12x^2+12x$
• $y^2=x^6+34x^5+2x^4+2x^3+11x^2+26x+19$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{37}$

The endomorphism algebra of this simple isogeny class is 4.0.55600.1.

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
2.37.s_fu	$2$	(not in LMFDB)