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

• Label: 2.37.aq_ew
• 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:	$1 - 16 x + 126 x^{2} - 592 x^{3} + 1369 x^{4}$
Frobenius angles:	$\pm0.108617277597$, $\pm0.378381097808$
Angle rank:	$2$ (numerical)
Number field:	4.0.76032.2
Galois group:	$D_{4}$
Jacobians:	$28$
Isomorphism classes:	44

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$888$	$1868352$	$2574646776$	$3511216333824$	$4807651383513528$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$22$	$1366$	$50830$	$1873486$	$69330502$	$2565705958$	$94932604222$	$3512486623774$	$129961769213302$	$4808584398142966$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=35x^6+5x^5+26x^4+27x^3+25x^2+9x+29$
• $y^2=10x^6+33x^5+31x^4+26x^3+11x^2+18x+27$
• $y^2=11x^6+15x^5+17x^4+36x^3+15x^2+35x+5$
• $y^2=21x^6+23x^5+24x^4+28x^3+35x^2+20x+3$
• $y^2=32x^6+24x^5+2x^4+33x^3+11x^2+36x+8$
• $y^2=22x^6+26x^5+26x^3+29x^2+28x+36$
• $y^2=16x^6+17x^5+16x^4+8x^3+36x^2+10x+35$
• $y^2=5x^6+15x^5+12x^4+9x^3+26x^2+10x+14$
• $y^2=20x^6+27x^5+6x^4+17x^3+7x^2+18x+15$
• $y^2=18x^6+12x^5+31x^4+12x^3+4x^2+4x+20$
• $y^2=18x^6+10x^5+3x^4+2x^2+29x+10$
• $y^2=9x^6+7x^5+4x^4+28x^2+36x+19$
• $y^2=16x^6+16x^5+36x^4+33x^3+26x^2+x+14$
• $y^2=26x^6+18x^5+28x^4+12x^2+26x+23$
• $y^2=20x^6+24x^5+5x^3+x^2+30x$
• $y^2=4x^6+32x^5+18x^4+24x^3+34x^2+13x+31$
• $y^2=15x^6+31x^5+15x^4+17x^3+13x^2+4x+14$
• $y^2=29x^6+36x^5+17x^4+35x^3+16x^2+8x+15$
• $y^2=31x^6+21x^5+14x^4+x^3+4x^2+9x+14$
• $y^2=2x^6+33x^5+9x^4+6x^3+30x^2+25x+14$
• $y^2=17x^6+3x^5+21x^4+5x^3+3x^2+3x+20$
• $y^2=6x^6+9x^5+x^3+8x^2+33x+18$
• $y^2=14x^6+33x^5+32x^4+10x^3+x^2+18x+20$
• $y^2=33x^6+15x^5+18x^4+11x^3+6x^2+7x+26$
• $y^2=32x^6+32x^5+31x^4+17x^3+29x^2+9x+20$
• $y^2=22x^6+9x^5+9x^4+19x^3+14x^2+8x+13$
• $y^2=10x^6+17x^5+22x^4+31x^3+28x^2+9x+4$
• $y^2=32x^6+32x^5+15x^4+15x^3+15x^2+27x+8$

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 4.0.76032.2.

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.q_ew	$2$	(not in LMFDB)