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

• Label: 2.79.abc_nd
• 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:	$1 - 28 x + 341 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.0441655312225$, $\pm0.301199111491$
Angle rank:	$2$ (numerical)
Number field:	4.0.212433.3
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	16

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4343$	$38318289$	$243114330176$	$1517084554914873$	$9468007191154511663$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$6140$	$493096$	$38949460$	$3076969012$	$243085981214$	$19203895779484$	$1517108753438308$	$119851596189202936$	$9468276087654879980$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=65x^6+8x^5+33x^4+31x^3+8x^2+14x+46$
• $y^2=57x^6+51x^5+56x^4+32x^3+69x^2+54x+51$
• $y^2=54x^6+22x^5+19x^4+69x^3+33x^2+52x+6$
• $y^2=23x^6+62x^5+45x^4+32x^3+10x^2+38x+8$
• $y^2=20x^6+2x^5+5x^4+64x^3+4x^2+13x+25$
• $y^2=38x^6+23x^5+46x^4+73x^3+52x^2+11x+58$
• $y^2=19x^6+40x^5+x^4+10x^3+58x^2+60x+6$
• $y^2=61x^6+77x^5+54x^4+76x^3+2x^2+74x+53$
• $y^2=71x^6+74x^5+24x^4+5x^3+29x^2+71x+51$
• $y^2=66x^6+17x^5+22x^4+4x^3+22x^2+38x+37$
• $y^2=34x^6+10x^5+67x^4+33x^3+48x^2+3x+33$
• $y^2=64x^6+23x^5+41x^4+65x^3+71x^2+48x+77$
• $y^2=12x^6+53x^5+29x^4+72x^3+40x^2+49x+71$
• $y^2=51x^6+77x^5+64x^4+26x^3+15x^2+12x+48$
• $y^2=37x^6+6x^5+20x^4+x^3+60x^2+66x+57$
• $y^2=68x^6+19x^5+18x^4+78x^3+47x^2+4x+78$

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 4.0.212433.3.

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_nd	$2$	(not in LMFDB)