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

• Label: 2.79.abe_om
• 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:	$1 - 30 x + 376 x^{2} - 2370 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.0386138984333$, $\pm0.255412854767$
Angle rank:	$2$ (numerical)
Number field:	4.0.65856.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4218$	$38037924$	$242953952850$	$1517163747825744$	$9468215618105027778$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$50$	$6094$	$492770$	$38951494$	$3077036750$	$243086618878$	$19203896306750$	$1517108688719614$	$119851595254257410$	$9468276081513605854$

Jacobians and polarizations

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

• $y^2=41x^6+60x^5+63x^4+54x^3+66x^2+62x+9$
• $y^2=77x^6+5x^5+36x^4+48x^3+9x^2+69x+35$
• $y^2=42x^6+20x^5+44x^4+30x^3+18x^2+70x+11$
• $y^2=70x^6+37x^5+54x^4+47x^3+77x^2+50x+29$
• $y^2=60x^6+54x^5+39x^4+49x^3+52x^2+49x+69$
• $y^2=69x^6+68x^5+64x^4+72x^3+62x^2+49x+53$
• $y^2=56x^6+4x^5+64x^4+47x^3+42x^2+40x+22$
• $y^2=70x^6+32x^5+2x^4+53x^3+40x^2+34x+2$
• $y^2=14x^6+3x^5+15x^4+10x^3+63x^2+26x+17$
• $y^2=22x^5+17x^4+58x^3+68x^2+42x+49$
• $y^2=14x^6+42x^5+54x^4+21x^3+12x^2+57x+57$
• $y^2=60x^6+41x^5+2x^4+72x^3+32x^2+18x+53$

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 4.0.65856.1.

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.be_om	$2$	(not in LMFDB)