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

• Label: 2.97.abg_qy
• 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:	$1 - 32 x + 440 x^{2} - 3104 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0743875887952$, $\pm0.274040761417$
Angle rank:	$2$ (numerical)
Number field:	4.0.825600.6
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6714$	$87188004$	$833117492826$	$7838034507384336$	$73742420670385691034$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$66$	$9266$	$912834$	$88536070$	$8587341186$	$832970899442$	$80798268258690$	$7837433500782334$	$760231059355917378$	$73742412713174175986$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=4 x^6+44 x^5+26 x^4+27 x^3+95 x^2+27 x+70$
• $y^2=47 x^6+30 x^5+6 x^4+77 x^3+63 x^2+36 x+95$
• $y^2=30 x^6+36 x^5+75 x^4+37 x^3+76 x^2+16 x+22$
• $y^2=52 x^6+49 x^5+52 x^4+79 x^3+5 x^2+89 x+28$
• $y^2=60 x^6+18 x^5+24 x^4+67 x^3+53 x^2+21 x+61$
• $y^2=7 x^6+62 x^5+57 x^4+96 x^3+93 x^2+x+61$
• $y^2=94 x^6+x^5+51 x^4+5 x^3+4 x^2+16 x+90$
• $y^2=27 x^6+18 x^5+56 x^4+31 x^3+4 x^2+26 x+56$
• $y^2=19 x^6+87 x^5+77 x^4+29 x^3+64 x^2+59 x+2$
• $y^2=17 x^6+26 x^5+8 x^4+46 x^3+72 x^2+37 x+26$
• $y^2=49 x^6+61 x^5+95 x^4+38 x^3+31 x^2+49 x+56$
• $y^2=32 x^6+15 x^5+4 x^4+19 x^3+90 x^2+54 x+1$
• $y^2=74 x^6+80 x^5+40 x^4+19 x^3+51 x^2+32 x+32$
• $y^2=29 x^6+85 x^5+19 x^4+70 x^3+33 x^2+67 x+14$
• $y^2=5 x^6+40 x^5+43 x^4+80 x^3+61 x^2+57 x+42$
• $y^2=46 x^6+37 x^5+94 x^4+29 x^3+42 x^2+67 x+63$

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 4.0.825600.6.

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_qy	$2$	(not in LMFDB)