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

• Label: 2.157.abq_bcn
• 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:	$1 - 42 x + 741 x^{2} - 6594 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0507848668956$, $\pm0.258189251026$
Angle rank:	$2$ (numerical)
Number field:	4.0.16410688.1
Galois group:	$D_{4}$
Jacobians:	$26$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18755$	$600666385$	$14974118708780$	$369150930553069225$	$9099054728885539902275$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$116$	$24368$	$3869390$	$607582644$	$95388938336$	$14976066185246$	$2351243155259072$	$369145193031254116$	$57955795537965868550$	$9099059901092647340768$

Jacobians and polarizations

This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=152x^6+99x^5+5x^4+8x^3+66x^2+49x+85$
• $y^2=115x^6+86x^5+75x^4+3x^3+83x^2+8x+84$
• $y^2=155x^6+48x^5+111x^4+97x^3+26x^2+106x+88$
• $y^2=102x^6+125x^5+131x^4+40x^3+42x^2+87x+125$
• $y^2=114x^6+x^5+126x^4+70x^3+68x^2+21x+134$
• $y^2=4x^6+83x^5+89x^4+26x^3+80x^2+94x+86$
• $y^2=74x^6+147x^5+14x^4+59x^3+137x^2+100x+43$
• $y^2=42x^6+91x^5+132x^4+98x^3+12x^2+56x+153$
• $y^2=107x^6+49x^5+36x^4+93x^3+29x^2+122x+2$
• $y^2=6x^6+69x^5+116x^4+88x^3+115x^2+13x+37$
• $y^2=79x^6+79x^5+60x^4+35x^3+52x^2+67x+11$
• $y^2=59x^6+2x^5+95x^4+102x^3+95x^2+45x+143$
• $y^2=127x^6+78x^5+94x^4+122x^3+65x^2+34x+63$
• $y^2=142x^6+34x^5+81x^4+58x^3+47x^2+152x+155$
• $y^2=5x^6+114x^5+83x^4+96x^3+11x^2+36x+146$
• $y^2=98x^6+45x^5+107x^4+54x^3+101x^2+28x+131$
• $y^2=24x^6+156x^5+24x^4+6x^3+134x^2+75x+70$
• $y^2=53x^6+69x^5+77x^4+45x^3+149x^2+151x+23$
• $y^2=112x^6+54x^5+65x^4+154x^3+64x^2+134x+149$
• $y^2=82x^6+110x^5+146x^4+123x^3+77x^2+148x+88$
• $y^2=8x^6+x^5+9x^4+18x^3+130x^2+38x+38$
• $y^2=150x^6+82x^5+142x^4+59x^3+145x^2+92x+136$
• $y^2=95x^6+13x^5+2x^4+60x^3+44x+120$
• $y^2=50x^6+9x^5+129x^4+100x^3+131x^2+15x+22$
• $y^2=91x^6+31x^5+85x^4+93x^3+51x^2+71x+23$
• $y^2=135x^6+81x^5+37x^4+59x^3+14x^2+151x+67$

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 4.0.16410688.1.

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.bq_bcn	$2$	(not in LMFDB)