Abelian variety isogeny class 2.83.abc_nl over $\F_{83}$

• Label: 2.83.abc_nl
• Base field: $\F_{83}$
• 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:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 28 x + 349 x^{2} - 2324 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0829582297929$, $\pm0.306761272556$
Angle rank:	$2$ (numerical)
Number field:	4.0.834353.1
Galois group:	$D_{4}$
Jacobians:	$34$
Isomorphism classes:	34

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4887$	$46871217$	$327164085504$	$2252457124903449$	$15515857998623455047$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$56$	$6804$	$572180$	$47461796$	$3938994136$	$326939362182$	$27136044280744$	$2252292265177924$	$186940256504422316$	$15516041201682604884$

Jacobians and polarizations

This isogeny class contains the Jacobians of 34 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=53x^6+79x^5+76x^4+62x^3+10x^2+26x+1$
• $y^2=8x^6+19x^5+41x^4+60x^3+71x^2+48x+80$
• $y^2=28x^6+45x^5+44x^4+39x^3+42x^2+40x+27$
• $y^2=43x^6+35x^5+59x^4+44x^3+15x^2+7x+6$
• $y^2=49x^6+37x^5+78x^4+21x^3+x^2+78x+55$
• $y^2=15x^6+73x^5+16x^4+49x^3+80x^2+65x+48$
• $y^2=43x^6+24x^5+31x^4+58x^3+35x^2+58x+24$
• $y^2=8x^6+43x^5+74x^4+53x^3+38x^2+14x+29$
• $y^2=56x^6+66x^5+16x^4+52x^2+19x+52$
• $y^2=32x^6+60x^4+14x^3+16x^2+28x+22$
• $y^2=80x^6+68x^4+12x^3+20x^2+66x+14$
• $y^2=31x^6+4x^5+31x^4+42x^3+65x^2+82x+19$
• $y^2=15x^6+76x^5+44x^4+47x^3+51x^2+42x+14$
• $y^2=5x^6+54x^5+70x^4+x^3+22x^2+34x+77$
• $y^2=47x^6+51x^5+37x^4+62x^3+22x^2+15x+39$
• $y^2=13x^6+10x^5+34x^4+74x^3+38x^2+67x+54$
• $y^2=77x^6+67x^5+40x^4+63x^3+82x^2+43x+32$
• $y^2=44x^6+76x^5+6x^4+58x^3+53x^2+28x+47$
• $y^2=24x^6+47x^5+10x^4+36x^3+72x^2+15x+54$
• $y^2=14x^6+11x^5+4x^4+11x^3+8x^2+73x+44$
• and

• $y^2=54x^6+39x^5+58x^4+46x^3+55x^2+42x+14$
• $y^2=12x^6+x^5+58x^4+42x^3+34x^2+29x+78$
• $y^2=51x^6+38x^5+57x^4+48x^3+76x^2+72x+63$
• $y^2=20x^6+24x^5+6x^4+61x^3+23x^2+62x+50$
• $y^2=6x^6+12x^5+57x^4+41x^3+6x^2+43x+19$
• $y^2=5x^6+37x^5+34x^4+81x^3+71x^2+73x+55$
• $y^2=17x^6+81x^5+18x^4+66x^3+53x^2+29x+9$
• $y^2=53x^6+16x^5+47x^4+71x^3+8x^2+39x+72$
• $y^2=72x^6+25x^5+32x^4+10x^3+7x^2+x+58$
• $y^2=40x^6+54x^5+46x^4+76x^3+32x^2+71x+23$
• $y^2=56x^6+54x^5+13x^4+46x^3+18x^2+58x+7$
• $y^2=69x^6+18x^5+51x^4+29x^3+18x^2+14x+72$
• $y^2=37x^6+78x^5+72x^4+62x^3+20x^2+72x+13$
• $y^2=67x^6+73x^5+59x^4+63x^3+81x^2+68x+42$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is 4.0.834353.1.

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
2.83.bc_nl	$2$	(not in LMFDB)