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

• Label: 2.79.abc_nq
• Base field: $\F_{79}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$( 1 - 14 x + 79 x^{2} )^{2}$
	$1 - 28 x + 354 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.211343260462$, $\pm0.211343260462$
Angle rank:	$1$ (numerical)
Jacobians:	$24$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4356$	$38489616$	$243654780996$	$1517968871654400$	$9468948043662723396$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$6166$	$494188$	$38972158$	$3077274772$	$243088768726$	$19203910119628$	$1517108722031998$	$119851594662830452$	$9468276071091907606$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=43x^6+30x^4+30x^2+43$
• $y^2=2x^5+18x^4+76x^3+60x^2+6x+6$
• $y^2=73x^6+70x^5+47x^4+64x^3+77x^2+8x+68$
• $y^2=39x^6+50x^5+32x^4+32x^3+42x^2+67x+60$
• $y^2=11x^6+28x^5+x^4+26x^3+32x^2+74x+50$
• $y^2=69x^6+73x^5+42x^4+53x^3+37x^2+18x+74$
• $y^2=27x^6+78x^5+62x^4+27x^3+23x^2+29x+70$
• $y^2=20x^6+72x^5+72x^4+50x^3+27x^2+39x+77$
• $y^2=30x^6+48x^5+25x^4+9x^3+75x^2+3x+56$
• $y^2=x^6+x^3+8$
• $y^2=60x^6+16x^5+72x^4+7x^3+32x^2+49x+29$
• $y^2=66x^6+65x^5+45x^4+56x^3+78x^2+29x+75$
• $y^2=14x^6+48x^5+8x^4+73x^3+18x^2+37x+12$
• $y^2=50x^6+8x^5+30x^4+74x^3+30x^2+8x+50$
• $y^2=74x^6+12x^5+73x^4+61x^3+73x^2+12x+74$
• $y^2=11x^6+37x^5+26x^4+63x^3+59x^2+37x+68$
• $y^2=41x^6+11x^5+58x^4+67x^3+58x^2+11x+41$
• $y^2=55x^6+11x^5+26x^4+68x^3+26x^2+11x+55$
• $y^2=73x^6+54x^4+54x^2+73$
• $y^2=27x^6+55x^5+69x^4+57x^3+69x^2+55x+27$
• $y^2=49x^6+4x^5+14x^4+47x^3+20x^2+39x+31$
• $y^2=x^6+73x^5+70x^4+57x^3+70x^2+73x+1$
• $y^2=x^6+72x^3+52$
• $y^2=34x^6+32x^5+67x^4+76x^3+32x^2+52x+37$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.ao^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-30}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.79.a_abm	$2$	(not in LMFDB)
2.79.bc_nq	$2$	(not in LMFDB)
2.79.o_en	$3$	(not in LMFDB)