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

• Label: 2.79.abd_od
• 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:	$1 - 29 x + 367 x^{2} - 2291 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.158489402170$, $\pm0.228705439247$
Angle rank:	$2$ (numerical)
Number field:	4.0.246725.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4289$	$38296481$	$243417215471$	$1517776436745389$	$9468854694963514224$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$51$	$6135$	$493707$	$38967219$	$3077244436$	$243088815171$	$19203914504889$	$1517108794796979$	$119851595460490053$	$9468276077188183150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=11x^6+49x^5+9x^4+71x^3+44x^2+5x+58$
• $y^2=43x^6+56x^5+28x^4+53x^3+61x^2+55x+44$
• $y^2=54x^6+69x^5+6x^4+70x^3+61x^2+36x+29$
• $y^2=68x^6+76x^5+21x^4+54x^3+22x^2+70x+3$
• $y^2=35x^6+17x^5+25x^4+66x^3+62x^2+61x+58$
• $y^2=71x^6+71x^5+40x^4+8x^3+6x^2+18x+28$

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 4.0.246725.1.

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_od	$2$	(not in LMFDB)