Abelian variety isogeny class 2.157.abs_bem over $\F_{157}$

• Label: 2.157.abs_bem
• Base field: $\F_{157}$
• 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:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$1 - 44 x + 792 x^{2} - 6908 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0704014652185$, $\pm0.215142566842$
Angle rank:	$2$ (numerical)
Number field:	4.0.4278528.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18490$	$598965060$	$14970795655930$	$369153343166019600$	$9099090745666998205450$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$114$	$24298$	$3868530$	$607586614$	$95389315914$	$14976074690746$	$2351243273519898$	$369145194035200606$	$57955795539305040690$	$9099059900983880740618$

Jacobians and polarizations

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

• $y^2=24x^6+4x^5+17x^4+34x^3+128x^2+53x+29$
• $y^2=127x^6+52x^5+29x^4+140x^3+63x^2+111x+2$
• $y^2=75x^6+20x^5+103x^4+54x^3+120x^2+25x+99$
• $y^2=69x^6+9x^5+82x^4+27x^3+20x^2+59x+48$
• $y^2=24x^6+93x^5+40x^4+65x^3+53x^2+133x+6$
• $y^2=151x^6+53x^5+142x^4+89x^3+7x^2+67x+149$
• $y^2=146x^6+37x^5+11x^4+91x^3+113x^2+19x+119$
• $y^2=138x^6+144x^5+11x^4+83x^3+138x^2+26x+123$
• $y^2=70x^6+115x^5+6x^4+72x^3+73x^2+37x+23$
• $y^2=76x^6+40x^5+4x^4+90x^3+58x^2+97x+114$
• $y^2=119x^6+130x^5+133x^4+70x^3+55x^2+80x+139$
• $y^2=49x^6+129x^5+61x^4+147x^3+140x^2+112x+149$
• $y^2=18x^6+37x^5+21x^4+132x^3+61x^2+89x+21$
• $y^2=133x^6+148x^5+14x^4+122x^3+82x^2+102x+58$
• $y^2=144x^6+147x^5+127x^4+49x^3+147x^2+24x+151$
• $y^2=85x^6+149x^5+139x^4+137x^3+155x^2+96x+140$
• $y^2=88x^6+98x^5+26x^4+25x^3+112x^2+75x+15$
• $y^2=142x^6+78x^5+95x^4+143x^3+113x^2+126x+83$
• $y^2=96x^6+109x^5+81x^4+94x^3+111x^2+109x+140$
• $y^2=85x^6+115x^5+65x^4+132x^3+19x^2+69x+2$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The endomorphism algebra of this simple isogeny class is 4.0.4278528.1.

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
2.157.bs_bem	$2$	(not in LMFDB)