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

• Label: 2.97.abf_qh
• 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:	$1 - 31 x + 423 x^{2} - 3007 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0934956278365$, $\pm0.288503720938$
Angle rank:	$2$ (numerical)
Number field:	4.0.195525.1
Galois group:	$D_{4}$
Jacobians:	$32$
Isomorphism classes:	40

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6795$	$87458445$	$833452690995$	$7838265914331525$	$73742536226340558000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$67$	$9295$	$913201$	$88538683$	$8587354642$	$832971140935$	$80798274920101$	$7837433618347123$	$760231060707307687$	$73742412722376848350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=26x^6+46x^4+89x^3+74x^2+88x+56$
• $y^2=55x^6+88x^5+85x^4+21x^3+94x^2+55x+18$
• $y^2=7x^6+15x^5+43x^4+82x^3+7x^2+91x+40$
• $y^2=22x^6+51x^5+83x^4+44x^2+85x+13$
• $y^2=18x^5+20x^4+8x^3+93x^2+56x+19$
• $y^2=78x^6+64x^5+10x^4+58x^3+51x^2+31x+81$
• $y^2=3x^6+28x^5+35x^4+10x^3+2x^2+48x+51$
• $y^2=40x^6+10x^5+56x^4+57x^3+12x^2+62x+2$
• $y^2=14x^6+79x^5+73x^4+11x^3+43x^2+80x+44$
• $y^2=38x^6+46x^5+26x^4+65x^3+56x^2+29x+26$
• $y^2=13x^6+47x^5+29x^4+85x^3+92x^2+13x+54$
• $y^2=80x^6+39x^5+81x^4+42x^3+89x^2+60x+40$
• $y^2=52x^6+28x^5+51x^4+84x^3+53x^2+51x+17$
• $y^2=20x^6+65x^5+18x^4+94x^3+66x^2+46x+24$
• $y^2=44x^6+38x^5+49x^4+72x^3+22x^2+9x+30$
• $y^2=3x^6+34x^5+18x^4+6x^3+75x^2+45x+41$
• $y^2=95x^6+94x^5+77x^4+62x^3+19x^2+3x+58$
• $y^2=59x^6+43x^5+95x^4+5x^3+21x^2+63x+45$
• $y^2=46x^6+38x^5+96x^4+28x^3+88x^2+46x+69$
• $y^2=68x^6+24x^5+55x^4+6x^3+55x^2+24x+45$
• and

• $y^2=15x^6+53x^5+60x^4+8x^3+84x+83$
• $y^2=83x^6+15x^5+4x^4+68x^3+66x^2+96x+10$
• $y^2=38x^6+17x^5+33x^4+77x^3+75x^2+34x+42$
• $y^2=13x^6+95x^5+67x^4+23x^3+38x^2+52x+14$
• $y^2=66x^6+79x^5+74x^4+87x^3+64x^2+9x+33$
• $y^2=52x^6+17x^5+66x^4+59x^3+31x^2+74x+28$
• $y^2=44x^6+16x^5+31x^4+48x^3+95x^2+69x+21$
• $y^2=93x^6+23x^5+92x^4+68x^3+77x+49$
• $y^2=68x^6+49x^5+34x^4+83x^3+15x^2+77x+82$
• $y^2=75x^6+76x^5+9x^4+22x^3+35x^2+41x+18$
• $y^2=57x^6+41x^5+38x^4+32x^3+91x^2+16x+37$
• $y^2=28x^6+64x^5+57x^4+16x^3+69x^2+70x+3$

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 4.0.195525.1.

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.bf_qh	$2$	(not in LMFDB)