Abelian variety isogeny class 2.137.abp_bar over $\F_{137}$

• Label: 2.137.abp_bar
• Base field: $\F_{137}$
• 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:	$\F_{137}$
Dimension:	$2$
L-polynomial:	$1 - 41 x + 693 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.125334691278$, $\pm0.189503359060$
Angle rank:	$2$ (numerical)
Number field:	4.0.347525.1
Galois group:	$D_{4}$
Jacobians:	$11$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$13805$	$346795405$	$6610490027405$	$124107569282705525$	$2329223182564580962000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$97$	$18475$	$2570821$	$352302723$	$48262328142$	$6611864583475$	$905824393318501$	$124097930636747043$	$17001416408198445817$	$2329194047539600200750$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 11 curves (of which all are hyperelliptic):

• $y^2=41 x^6+94 x^5+70 x^4+85 x^3+71 x^2+20 x+23$
• $y^2=89 x^6+128 x^5+47 x^4+63 x^3+6 x^2+49 x+43$
• $y^2=85 x^6+132 x^5+111 x^4+131 x^3+102 x^2+93 x+77$
• $y^2=52 x^6+122 x^5+26 x^4+50 x^3+132 x^2+104 x+33$
• $y^2=86 x^6+106 x^5+96 x^4+x^3+135 x^2+62 x+104$
• $y^2=131 x^6+117 x^5+43 x^4+81 x^3+60 x^2+11 x+67$
• $y^2=11 x^6+62 x^5+124 x^4+101 x^3+104 x^2+3 x+72$
• $y^2=98 x^6+16 x^5+48 x^4+90 x^3+43 x^2+78 x$
• $y^2=88 x^6+72 x^5+67 x^4+51 x^3+62 x^2+8 x+49$
• $y^2=83 x^6+49 x^5+76 x^4+94 x^3+71 x^2+54 x+83$
• $y^2=41 x^6+82 x^5+10 x^4+119 x^3+125 x^2+18 x+67$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{137}$.

Endomorphism algebra over $\F_{137}$

The endomorphism algebra of this simple isogeny class is 4.0.347525.1.

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
2.137.bp_bar	$2$	(not in LMFDB)