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

• Label: 2.139.abn_yt
• 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:	$1 - 39 x + 643 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.0387522107239$, $\pm0.269975319668$
Angle rank:	$2$ (numerical)
Number field:	4.0.1060485.1
Galois group:	$D_{4}$
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14505$	$368789625$	$7211603834235$	$139354891480738125$	$2692443551032058672400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$101$	$19087$	$2685269$	$373304323$	$51888677936$	$7212543437347$	$1002544267169819$	$139353666137590003$	$19370159736471430031$	$2692452204221961814102$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=33x^6+8x^5+65x^4+53x^3+101x^2+43x+114$
• $y^2=17x^6+53x^5+134x^4+105x^3+116x^2+84x+131$
• $y^2=61x^6+24x^5+80x^4+87x^3+132x^2+93x+43$
• $y^2=62x^6+133x^5+122x^4+57x^3+91x^2+116x+15$
• $y^2=134x^6+96x^5+78x^4+98x^3+62x^2+132x+5$
• $y^2=10x^6+107x^5+43x^4+92x^3+102x^2+53x+23$
• $y^2=101x^6+7x^5+13x^4+48x^3+132x^2+38x+53$
• $y^2=71x^6+90x^5+28x^4+38x^3+19x^2+114x+21$
• $y^2=109x^6+84x^5+78x^4+27x^3+18x^2+25x+131$
• $y^2=65x^6+47x^5+66x^4+13x^3+69x^2+133x+112$
• $y^2=94x^6+101x^5+9x^4+123x^3+40x^2+135x+48$
• $y^2=119x^6+114x^5+92x^4+64x^3+120x^2+79x+134$
• $y^2=44x^6+127x^5+123x^4+84x^3+98x^2+121x+69$
• $y^2=132x^6+92x^5+86x^4+125x^3+49x^2+7x+67$
• $y^2=23x^6+38x^5+71x^4+11x^3+5x^2+133x+69$
• $y^2=57x^6+29x^5+98x^4+27x^3+28x^2+24x+32$
• $y^2=50x^6+96x^5+21x^4+109x^3+7x^2+52x+66$
• $y^2=95x^6+90x^5+12x^4+9x^3+125x^2+135x+41$
• $y^2=16x^6+39x^5+128x^4+61x^3+107x^2+5x+121$
• $y^2=73x^6+38x^5+49x^4+120x^3+114x^2+92x+70$

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 4.0.1060485.1.

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_yt	$2$	(not in LMFDB)