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

• Label: 2.97.abg_ra
• 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:	$1 - 32 x + 442 x^{2} - 3104 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.0949181811045$, $\pm0.266857352358$
Angle rank:	$2$ (numerical)
Number field:	4.0.28736.2
Galois group:	$D_{4}$
Jacobians:	$40$
Isomorphism classes:	50

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6716$	$87227408$	$833293240700$	$7838447480996864$	$73743077434139795196$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$66$	$9270$	$913026$	$88540734$	$8587417666$	$832971830070$	$80798276903298$	$7837433561793534$	$760231059688866882$	$73742412715125383350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=71x^6+36x^5+83x^4+4x^3+85x^2+66x+21$
• $y^2=45x^6+37x^5+48x^4+83x^3+89x^2+28x+92$
• $y^2=78x^6+91x^5+57x^4+6x^3+59x^2+82x+58$
• $y^2=37x^6+75x^5+24x^4+30x^3+34x^2+92x+37$
• $y^2=6x^5+33x^4+17x^3+34x^2+53x+38$
• $y^2=58x^6+10x^5+11x^4+71x^3+44x^2+55x+42$
• $y^2=21x^6+66x^5+48x^4+11x^3+94x^2+88x+53$
• $y^2=76x^6+62x^5+72x^4+44x^3+19x^2+44x+23$
• $y^2=17x^6+27x^5+8x^4+58x^3+94x^2+13x+72$
• $y^2=69x^6+54x^5+32x^4+52x^3+71x^2+11x+80$
• $y^2=88x^6+95x^5+85x^4+66x^3+25x^2+15x+56$
• $y^2=58x^6+57x^5+33x^4+75x^3+30x^2+16x+48$
• $y^2=14x^6+9x^5+43x^4+92x^3+78x^2+78x+32$
• $y^2=68x^6+13x^5+76x^4+39x^3+49x^2+62x+6$
• $y^2=58x^6+11x^5+72x^4+19x^3+93x^2+74x+52$
• $y^2=15x^6+92x^5+59x^4+33x^3+86x^2+67x+14$
• $y^2=37x^6+8x^5+57x^4+40x^3+70x^2+45x+93$
• $y^2=59x^6+90x^5+3x^4+13x^3+74x^2+84x+57$
• $y^2=70x^6+93x^5+10x^4+13x^3+20x^2+15x+46$
• $y^2=59x^6+79x^5+70x^4+55x^3+49x^2+66$
• and

• $y^2=42x^6+12x^5+9x^4+x^3+14x^2+38x+70$
• $y^2=84x^6+13x^5+69x^4+74x^3+84x^2+78x+64$
• $y^2=18x^6+47x^5+55x^4+81x^3+43x^2+66x+41$
• $y^2=3x^6+3x^5+60x^4+37x^3+57x^2+82x+78$
• $y^2=10x^6+57x^5+37x^4+16x^3+42x^2+58x+76$
• $y^2=84x^6+11x^5+78x^4+38x^3+51x^2+76x+57$
• $y^2=12x^6+70x^5+90x^4+11x^3+93x^2+54x+92$
• $y^2=10x^6+76x^5+35x^4+51x^3+63x^2+16x+92$
• $y^2=91x^6+69x^5+70x^4+3x^3+24x^2+48x+7$
• $y^2=73x^6+80x^5+12x^4+80x^3+5x^2+12x+84$
• $y^2=34x^6+25x^5+37x^4+37x^3+41x^2+12x+24$
• $y^2=92x^6+22x^5+65x^4+28x^3+49x^2+57x+92$
• $y^2=23x^6+53x^5+21x^4+5x^3+9x^2+21x+52$
• $y^2=28x^6+20x^5+35x^4+62x^3+43x^2+4x+23$
• $y^2=55x^6+87x^5+23x^4+2x^3+49x^2+53x+71$
• $y^2=80x^6+72x^5+x^4+78x^3+91x^2+39x+82$
• $y^2=37x^6+16x^5+44x^3+86x^2+48x+34$
• $y^2=62x^6+91x^5+62x^4+73x^3+34x^2+6x+17$
• $y^2=30x^6+18x^5+8x^4+43x^3+10x^2+62x+65$
• $y^2=11x^6+62x^5+58x^4+17x^3+5x^2+71x+48$

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 4.0.28736.2.

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_ra	$2$	(not in LMFDB)