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

• Label: 2.79.abc_nf
• 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:	$1 - 28 x + 343 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.0725523305001$, $\pm0.294774414398$
Angle rank:	$2$ (numerical)
Number field:	4.0.6305552.1
Galois group:	$D_{4}$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4345$	$38344625$	$243197453620$	$1517222307643625$	$9468161412621301225$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$6144$	$493264$	$38952996$	$3077019132$	$243086519622$	$19203900611668$	$1517108795811396$	$119851596622783216$	$9468276092702681824$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=43x^6+5x^5+18x^4+31x^3+65x^2+11x+20$
• $y^2=48x^6+76x^5+15x^4+31x^3+39x^2+74x+58$
• $y^2=66x^6+32x^5+68x^4+11x^3+50x^2+49x+35$
• $y^2=x^6+73x^5+31x^4+3x^3+64x^2+71x+43$
• $y^2=35x^6+77x^5+71x^4+2x^3+69x^2+34x+3$
• $y^2=27x^6+8x^5+12x^4+51x^3+51x^2+71x+63$
• $y^2=43x^6+48x^5+72x^4+44x^3+25x+58$
• $y^2=25x^6+10x^5+45x^4+30x^3+8x^2+17x+5$
• $y^2=28x^6+16x^5+39x^4+49x^3+45x^2+11$
• $y^2=7x^6+38x^5+69x^4+41x^3+62x^2+3x+56$

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 4.0.6305552.1.

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.bc_nf	$2$	(not in LMFDB)