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

• Label: 2.97.abj_tf
• 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:	$1 - 35 x + 499 x^{2} - 3395 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.105878802195$, $\pm0.187386122344$
Angle rank:	$2$ (numerical)
Number field:	4.0.123725.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6479$	$86423381$	$832366518071$	$7838213566376501$	$73744119873016276464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$63$	$9183$	$912009$	$88538091$	$8587539058$	$832974445407$	$80798306857149$	$7837433751887283$	$760231059415198203$	$73742412690531706078$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=69x^6+45x^5+69x^4+29x^3+58x^2+53x+55$
• $y^2=61x^6+16x^5+35x^4+8x^3+69x^2+71x+10$
• $y^2=39x^6+58x^5+38x^4+40x^3+27x^2+84x+23$
• $y^2=32x^6+19x^5+55x^4+76x^3+79x^2+15x+15$
• $y^2=60x^6+23x^5+21x^4+38x^3+93x^2+74x+45$
• $y^2=8x^6+77x^5+52x^4+67x^3+73x^2+25x+92$

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 4.0.123725.1.

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.bj_tf	$2$	(not in LMFDB)