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

• Label: 2.137.abn_yv
• 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:	$1 - 39 x + 645 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.0869532210059$, $\pm0.251808753161$
Angle rank:	$2$ (numerical)
Number field:	4.0.15131557.1
Galois group:	$D_{4}$
Jacobians:	$10$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14033$	$347976301$	$6612157193537$	$124105066066076341$	$2329204294369226148608$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$99$	$18539$	$2571471$	$352295619$	$48261936774$	$6611856425939$	$905824282264623$	$124097929670110243$	$17001416406443177835$	$2329194047657402219054$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=62x^6+60x^5+31x^4+68x^3+12x^2+4x+70$
• $y^2=30x^6+39x^5+107x^4+94x^3+132x^2+20x+35$
• $y^2=27x^6+20x^5+x^4+130x^3+18x^2+87x+28$
• $y^2=124x^6+23x^5+79x^4+51x^3+127x^2+66x+124$
• $y^2=132x^6+74x^5+49x^4+51x^3+x^2+110x+74$
• $y^2=13x^6+107x^5+24x^4+82x^3+12x^2+101x+28$
• $y^2=51x^6+79x^5+102x^4+130x^3+118x^2+3x+67$
• $y^2=97x^6+59x^5+51x^4+45x^3+134x^2+56x+51$
• $y^2=46x^6+7x^5+34x^4+41x^3+80x^2+4x+119$
• $y^2=27x^6+53x^5+128x^4+99x^3+66x^2+41x+15$

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 4.0.15131557.1.

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_yv	$2$	(not in LMFDB)