Abelian variety isogeny class 2.97.abg_rb over $\F_{97}$

• Label: 2.97.abg_rb
• Base field: $\F_{97}$
• 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:	$\F_{97}$
Dimension:	$2$
L-polynomial:	$1 - 32 x + 443 x^{2} - 3104 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.104498415736$, $\pm0.262864569503$
Angle rank:	$2$ (numerical)
Number field:	4.0.6630288.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6717$	$87247113$	$833381118612$	$7838653438833849$	$73743401694806105637$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$66$	$9272$	$913122$	$88543060$	$8587455426$	$832972275686$	$80798280674562$	$7837433580562660$	$760231059654292002$	$73742412713250050312$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which all are hyperelliptic):

• $y^2=61 x^6+3 x^5+81 x^4+48 x^3+6 x^2+9 x+7$
• $y^2=87 x^6+40 x^5+57 x^4+81 x^3+33 x^2+10 x+9$
• $y^2=71 x^6+26 x^5+76 x^4+5 x^3+36 x^2+52 x+64$
• $y^2=58 x^6+59 x^5+24 x^4+19 x^3+84 x^2+88 x+4$
• $y^2=83 x^6+13 x^5+91 x^4+87 x^3+71 x^2+50 x+23$
• $y^2=23 x^6+39 x^5+15 x^4+61 x^3+62 x^2+88 x+66$
• $y^2=71 x^6+49 x^5+18 x^4+5 x^3+5 x^2+76 x+96$
• $y^2=71 x^6+80 x^5+25 x^4+86 x^3+17 x^2+60 x+92$
• $y^2=2 x^6+65 x^5+55 x^4+50 x^3+93 x^2+65 x+71$
• $y^2=36 x^6+65 x^5+2 x^4+13 x^3+6 x^2+33 x+26$
• $y^2=28 x^6+55 x^5+58 x^4+83 x^3+3 x^2+66 x+69$
• $y^2=47 x^6+32 x^5+40 x^4+58 x^3+48 x^2+25 x+67$
• $y^2=64 x^6+56 x^5+39 x^4+47 x^3+59 x^2+71 x+80$
• $y^2=28 x^6+82 x^5+38 x^4+46 x^3+16 x^2+6 x+7$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$

The endomorphism algebra of this simple isogeny class is 4.0.6630288.1.

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
2.97.bg_rb	$2$	(not in LMFDB)