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

• Label: 2.157.abs_beq
• 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:	$1 - 44 x + 796 x^{2} - 6908 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.116000093546$, $\pm0.193158636467$
Angle rank:	$2$ (numerical)
Number field:	4.0.1042688.2
Galois group:	$D_{4}$
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18494$	$599168612$	$14972842581998$	$369164445930636944$	$9099133136795892008574$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$114$	$24306$	$3869058$	$607604886$	$95389760314$	$14976083096418$	$2351243401541946$	$369145195585347294$	$57955795552734381714$	$9099059901020192623666$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=149x^6+148x^5+150x^4+35x^3+27x^2+37x+134$
• $y^2=12x^6+71x^5+109x^4+41x^3+75x^2+128x+82$
• $y^2=140x^6+55x^5+68x^4+140x^3+2x^2+43x+43$
• $y^2=83x^6+68x^5+21x^4+148x^3+21x^2+88x+45$
• $y^2=94x^6+70x^5+42x^4+84x^3+70x^2+61x+7$
• $y^2=146x^6+132x^5+114x^4+17x^3+98x^2+109x+149$
• $y^2=86x^5+125x^4+127x^3+56x^2+115x+141$
• $y^2=6x^6+154x^5+91x^4+119x^3+142x^2+131x+74$
• $y^2=29x^6+141x^5+115x^4+37x^3+40x^2+112x+66$
• $y^2=8x^6+50x^5+66x^4+137x^3+14x^2+148x+154$
• $y^2=59x^6+32x^5+93x^4+48x^3+3x^2+48x+102$
• $y^2=18x^6+56x^5+63x^4+15x^3+37x^2+77x+58$
• $y^2=65x^6+16x^5+97x^4+17x^3+137x^2+94x+22$
• $y^2=35x^6+17x^5+32x^4+83x^3+149x^2+126x+7$
• $y^2=88x^6+102x^5+72x^4+10x^3+71x^2+52x+128$
• $y^2=74x^6+121x^5+127x^4+71x^3+48x^2+14$
• $y^2=137x^6+20x^5+25x^4+101x^3+69x^2+135x+146$
• $y^2=103x^6+18x^5+7x^4+126x^3+20x^2+130x+97$

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 4.0.1042688.2.

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_beq	$2$	(not in LMFDB)