Abelian variety isogeny class 2.79.abd_nu over $\F_{79}$

• Label: 2.79.abd_nu
• Base field: $\F_{79}$
• 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:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$1 - 29 x + 358 x^{2} - 2291 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.0292162286946$, $\pm0.280758227595$
Angle rank:	$2$ (numerical)
Number field:	4.0.8405.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4280$	$38177600$	$243029579360$	$1517105286560000$	$9468071648946131400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$51$	$6117$	$492924$	$38949993$	$3076989961$	$243086075022$	$19203893256879$	$1517108696320113$	$119851595571614196$	$9468276083951594077$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=31x^6+11x^5+35x^4+49x^3+73x^2+32x+6$
• $y^2=24x^6+22x^5+16x^4+39x^3+62x^2+27x+28$
• $y^2=39x^6+64x^5+20x^4+46x^3+6x^2+10x+44$
• $y^2=34x^6+68x^4+45x^3+x^2+78x+54$
• $y^2=76x^6+19x^5+9x^4+14x^3+39x^2+44x$
• $y^2=11x^6+70x^5+14x^4+58x^3+46x^2+13x+24$
• $y^2=59x^6+52x^5+39x^4+65x^3+5x^2+15x+43$
• $y^2=75x^6+41x^5+74x^4+70x^3+27x^2+37x+49$
• $y^2=x^6+6x^5+21x^4+76x^3+65x^2+42x+32$
• $y^2=14x^6+76x^5+65x^4+20x^3+75x^2+64x+71$
• $y^2=56x^6+44x^5+22x^4+44x^3+28x^2+39x+34$
• $y^2=4x^6+2x^5+58x^4+45x^3+42x^2+69x+59$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79}$.

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is 4.0.8405.1.

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
2.79.bd_nu	$2$	(not in LMFDB)