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

• Label: 2.137.abq_bbi
• 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:	$1 - 42 x + 710 x^{2} - 5754 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.0387594407114$, $\pm0.204006140474$
Angle rank:	$2$ (numerical)
Number field:	4.0.39600.1
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$13684$	$345876784$	$6606998222836$	$124097319488330496$	$2329197815680791488884$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$96$	$18426$	$2569464$	$352273630$	$48261802536$	$6611856341082$	$905824280205360$	$124097929287834814$	$17001416394624755088$	$2329194047434250395386$

Jacobians and polarizations

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

• $y^2=42x^5+34x^4+58x^3+85x^2+127x+108$
• $y^2=44x^6+52x^5+69x^4+37x^3+82x^2+51x+88$
• $y^2=108x^6+67x^5+121x^4+18x^3+117x^2+23x+108$
• $y^2=114x^6+19x^5+111x^4+121x^3+109x^2+26x$
• $y^2=86x^6+20x^5+116x^4+95x^3+95x^2+120x+98$
• $y^2=43x^6+105x^5+81x^4+76x^3+19x^2+10x+34$
• $y^2=29x^6+51x^5+127x^4+76x^3+94x^2+56x+71$
• $y^2=3x^6+95x^5+7x^4+65x^3+91x^2+78x+117$
• $y^2=21x^6+63x^5+128x^4+14x^3+80x^2+61x+71$
• $y^2=46x^6+93x^5+123x^4+18x^3+65x^2+58x+63$
• $y^2=124x^6+39x^5+81x^4+33x^3+114x^2+11x+9$
• $y^2=98x^6+4x^5+59x^4+30x^3+92x^2+68x+106$

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 4.0.39600.1.

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.bq_bbi	$2$	(not in LMFDB)