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

• Label: 2.157.abu_bgi
• 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:	$1 - 46 x + 840 x^{2} - 7222 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0515472603327$, $\pm0.177395699406$
Angle rank:	$2$ (numerical)
Number field:	4.0.412992.5
Galois group:	$D_{4}$
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18222$	$596916276$	$14964151176126$	$369139636523072976$	$9099074508281416709502$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$112$	$24214$	$3866812$	$607564054$	$95389145692$	$14976075048694$	$2351243306799520$	$369145194548377438$	$57955795541751486976$	$9099059900904009245254$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):

• $y^2=125 x^6+49 x^5+144 x^4+141 x^2+132 x+76$
• $y^2=152 x^6+152 x^5+103 x^4+61 x^3+74 x^2+60 x+154$
• $y^2=96 x^6+95 x^5+118 x^4+115 x^3+94 x^2+65 x+23$
• $y^2=72 x^6+111 x^5+8 x^4+77 x^3+156 x^2+89 x+51$
• $y^2=89 x^6+122 x^5+2 x^4+30 x^3+99 x^2+135 x+23$
• $y^2=123 x^6+53 x^5+130 x^4+27 x^3+57 x^2+126 x+120$
• $y^2=98 x^6+125 x^5+75 x^4+135 x^3+41 x^2+152 x+7$
• $y^2=45 x^6+146 x^5+21 x^4+147 x^3+70 x^2+84 x+20$

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 4.0.412992.5.

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.bu_bgi	$2$	(not in LMFDB)