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

• Label: 2.137.abn_yp
• 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:	$1 - 39 x + 639 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.00608336417129$, $\pm0.267928225148$
Angle rank:	$2$ (numerical)
Number field:	4.0.226981.1
Galois group:	$C_4$
Jacobians:	$1$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14027$	$347743357$	$6610348772651$	$124097633743721989$	$2329183175938050519152$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$99$	$18527$	$2570769$	$352274523$	$48261499194$	$6611849436647$	$905824191029661$	$124097928637117171$	$17001416395180327743$	$2329194047520161837582$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is hyperelliptic):

• $y^2=106 x^6+61 x^5+77 x^4+118 x^3+136 x^2+23 x+107$

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 4.0.226981.1.

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.bn_yp	$2$	(not in LMFDB)