Abelian variety isogeny class 2.139.abn_yu over $\F_{139}$

• Label: 2.139.abn_yu
• Base field: $\F_{139}$
• 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:	$\F_{139}$
Dimension:	$2$
L-polynomial:	$1 - 39 x + 644 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.0512302470248$, $\pm0.267624205263$
Angle rank:	$2$ (numerical)
Number field:	4.0.14321592.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14506$	$368829556$	$7211918601832$	$139356201880518048$	$2692447325174472076966$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$101$	$19089$	$2685386$	$373307833$	$51888750671$	$7212544605906$	$1002544282836197$	$139353666328482289$	$19370159738857786718$	$2692452204255518893089$

Jacobians and polarizations

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

• $y^2=16x^6+111x^5+129x^4+133x^3+68x^2+42x+125$
• $y^2=124x^6+42x^5+69x^4+75x^3+67x^2+72x+26$
• $y^2=59x^6+120x^5+10x^4+4x^3+135x^2+5x+86$
• $y^2=61x^6+53x^5+42x^4+73x^3+24x^2+65x+83$
• $y^2=64x^6+97x^5+53x^4+131x^3+126x^2+79x+46$
• $y^2=95x^6+2x^5+31x^4+14x^3+127x^2+68x+133$
• $y^2=84x^6+44x^5+30x^4+4x^2+99x+12$
• $y^2=89x^6+115x^5+73x^4+30x^3+22x^2+61x+95$
• $y^2=33x^6+22x^5+53x^4+11x^3+7x^2+84x+97$
• $y^2=114x^6+71x^5+101x^4+25x^3+33x^2+120x+76$
• $y^2=120x^6+99x^5+60x^4+41x^3+120x^2+121x+123$
• $y^2=134x^6+67x^5+55x^4+5x^3+2x^2+34x+75$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{139}$.

Endomorphism algebra over $\F_{139}$

The endomorphism algebra of this simple isogeny class is 4.0.14321592.1.

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
2.139.bn_yu	$2$	(not in LMFDB)