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

• Label: 2.79.am_hm
• 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:	$( 1 - 6 x + 79 x^{2} )^{2}$
	$1 - 12 x + 194 x^{2} - 948 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.390409785279$, $\pm0.390409785279$
Angle rank:	$1$ (numerical)
Jacobians:	$50$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$5476$	$40500496$	$244279108516$	$1516921777382400$	$9467601080795397796$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$68$	$6486$	$495452$	$38945278$	$3076837028$	$243086518806$	$19203920696252$	$1517108954167678$	$119851595923087748$	$9468276070873035606$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 50 curves (of which all are hyperelliptic):

• $y^2=4 x^5+x^4+28 x^3+25 x^2+60 x+47$
• $y^2=34 x^6+74 x^5+62 x^4+19 x^3+62 x^2+74 x+34$
• $y^2=68 x^6+51 x^5+25 x^4+15 x^3+2 x^2+16 x+47$
• $y^2=46 x^6+51 x^5+17 x^4+77 x^3+77 x^2+9 x+35$
• $y^2=43 x^6+5 x^5+72 x^4+49 x^3+70 x^2+10 x+51$
• $y^2=7 x^6+48 x^5+28 x^4+31 x^3+44 x^2+17 x+29$
• $y^2=44 x^6+41 x^5+66 x^4+60 x^3+66 x^2+41 x+44$
• $y^2=36 x^6+5 x^5+43 x^4+34 x^3+17 x+59$
• $y^2=17 x^6+2 x^4+2 x^2+17$
• $y^2=36 x^6+7 x^5+72 x^4+6 x^3+72 x^2+62 x+48$
• $y^2=10 x^6+59 x^5+49 x^4+25 x^3+36 x^2+58 x+43$
• $y^2=2 x^5+70 x^4+44 x^3+70 x^2+2 x$
• $y^2=47 x^6+67 x^5+20 x^4+6 x^3+2 x^2+22 x+48$
• $y^2=61 x^6+69 x^5+10 x^4+75 x^3+51 x^2+64 x+2$
• $y^2=18 x^6+57 x^5+34 x^4+49 x^3+53 x^2+78 x+24$
• $y^2=73 x^6+61 x^5+28 x^4+77 x^3+31 x^2+77 x+53$
• $y^2=63 x^6+41 x^5+32 x^4+3 x^3+14 x^2+30 x+14$
• $y^2=3 x^6+7 x^5+55 x^4+25 x^3+76 x^2+76 x+53$
• $y^2=64 x^6+69 x^5+73 x^4+45 x^3+73 x^2+69 x+64$
• $y^2=11 x^6+73 x^5+7 x^4+40 x^3+57 x^2+62$
• and

• $y^2=43 x^6+62 x^5+59 x^4+49 x^3+20 x^2+58 x+47$
• $y^2=39 x^6+67 x^5+18 x^4+49 x^3+30 x^2+50 x+72$
• $y^2=62 x^6+62 x^5+73 x^4+48 x^3+4 x^2+10 x+46$
• $y^2=69 x^6+72 x^5+42 x^4+8 x^3+8 x^2+37 x+64$
• $y^2=32 x^6+22 x^4+22 x^2+32$
• $y^2=71 x^6+12 x^5+50 x^4+29 x^3+47 x^2+41 x+48$
• $y^2=57 x^6+30 x^5+76 x^4+39 x^3+26 x^2+21 x+17$
• $y^2=43 x^6+59 x^5+x^4+47 x^3+27 x^2+30 x+48$
• $y^2=27 x^5+18 x^4+50 x^3+21 x^2+1$
• $y^2=58 x^6+53 x^5+49 x^4+59 x^3+68 x^2+14 x+70$
• $y^2=26 x^6+28 x^5+11 x^4+18 x^3+52 x^2+12 x+26$
• $y^2=78 x^6+73 x^4+49 x^3+74 x^2+33 x+33$
• $y^2=60 x^6+58 x^4+4 x^3+59 x^2+49 x+72$
• $y^2=74 x^6+39 x^5+52 x^4+32 x^3+73 x^2+45 x+24$
• $y^2=68 x^6+56 x^5+8 x^4+74 x^3+54 x^2+44 x+22$
• $y^2=49 x^6+27 x^5+43 x^4+38 x^3+4 x^2+47 x+72$
• $y^2=55 x^6+25 x^5+37 x^4+38 x^3+18 x^2+36 x+13$
• $y^2=28 x^6+75 x^5+58 x^4+36 x^3+7 x^2+70 x+2$
• $y^2=39 x^6+12 x^5+27 x^4+2 x^3+60 x^2+43 x+60$
• $y^2=47 x^6+32 x^5+21 x^4+74 x^3+52 x^2+46 x+55$
• $y^2=33 x^6+33 x^5+40 x^4+47 x^3+40 x^2+33 x+33$
• $y^2=52 x^5+54 x^4+18 x^3+40 x^2+62 x+21$
• $y^2=64 x^6+56 x^5+72 x^4+39 x^3+72 x^2+56 x+64$
• $y^2=19 x^6+47 x^5+72 x^4+71 x^3+47 x^2+24 x+59$
• $y^2=45 x^6+14 x^5+78 x^4+76 x^3+78 x^2+14 x+45$
• $y^2=57 x^6+43 x^5+51 x^4+78 x^2+47 x+46$
• $y^2=69 x^6+53 x^5+18 x^4+72 x^3+12 x^2+3 x+75$
• $y^2=53 x^6+61 x^5+3 x^4+6 x^3+66 x^2+44 x+60$
• $y^2=53 x^6+2 x^5+76 x^4+13 x^3+44 x^2+4 x$
• $y^2=42 x^6+4 x^5+12 x^4+42 x^3+57 x^2+31 x+55$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.ag^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-70}) \)$)$

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_es	$2$	(not in LMFDB)
2.79.m_hm	$2$	(not in LMFDB)
2.79.g_abr	$3$	(not in LMFDB)