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

• Label: 2.137.abn_yw
• 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:	$1 - 39 x + 646 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.0951044323561$, $\pm0.248558856465$
Angle rank:	$2$ (numerical)
Number field:	4.0.14039388.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14034$	$348015132$	$6612458610528$	$124106299865636544$	$2329207748235794776674$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$99$	$18541$	$2571588$	$352299121$	$48262008339$	$6611857522018$	$905824295083611$	$124097929778451169$	$17001416406924623124$	$2329194047654407463341$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=90x^6+67x^5+88x^4+75x^3+7x^2+82x+70$
• $y^2=100x^6+50x^5+118x^4+75x^3+8x^2+128x+73$
• $y^2=86x^6+71x^5+82x^4+88x^3+5x^2+40x+68$
• $y^2=34x^6+46x^5+14x^4+82x^3+112x^2+16x+114$
• $y^2=10x^6+94x^5+20x^4+114x^3+7x^2+99$
• $y^2=23x^6+56x^5+90x^4+135x^3+84x^2+33x+13$
• $y^2=114x^6+71x^5+29x^4+39x^3+85x^2+105x+13$
• $y^2=16x^6+88x^5+66x^4+35x^3+81x^2+58x+90$
• $y^2=111x^6+122x^5+38x^4+25x^3+125x^2+14x+110$
• $y^2=113x^6+94x^5+107x^4+96x^3+100x^2+22x+96$
• $y^2=47x^6+39x^5+39x^4+125x^3+53x^2+123x+30$
• $y^2=71x^6+40x^5+9x^4+10x^3+72x^2+39x+30$
• $y^2=79x^6+100x^5+118x^4+46x^3+71x^2+66x+33$
• $y^2=4x^6+24x^5+78x^4+12x^3+22x^2+101x+34$
• $y^2=134x^6+29x^5+29x^4+52x^3+61x^2+115x+33$
• $y^2=x^6+32x^5+7x^4+44x^3+131x^2+80x+58$
• $y^2=3x^6+58x^5+40x^4+73x^3+65x^2+111x+9$
• $y^2=104x^6+25x^5+74x^4+18x^3+48x^2+49x+48$
• $y^2=10x^6+57x^5+81x^4+131x^3+29x^2+88x+31$
• $y^2=6x^6+86x^5+88x^4+114x^3+68x^2+130x+58$
• $y^2=94x^6+89x^5+104x^4+136x^3+117x^2+5x+127$
• $y^2=85x^6+31x^5+62x^4+78x^3+79x^2+79x+48$
• $y^2=31x^6+118x^5+58x^4+110x^3+41x^2+31x+12$
• $y^2=66x^6+71x^5+80x^4+67x^3+62x^2+26x+103$

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 4.0.14039388.1.

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_yw	$2$	(not in LMFDB)