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

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

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$1 + 24 x + 288 x^{2} + 1896 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.653790398454$, $\pm0.846209601546$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(i, \sqrt{14})\)
Galois group:	$C_2^2$
Jacobians:	$66$
Isomorphism classes:	68
Cyclic group of points:	no
Non-cyclic primes:	$13$

This isogeny class is simple but not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8450$	$38954500$	$242484723650$	$1517453070250000$	$9468247355271877250$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$104$	$6242$	$491816$	$38958918$	$3077047064$	$243087455522$	$19203902560856$	$1517108926669438$	$119851595089062824$	$9468276082626847202$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 66 curves (of which all are hyperelliptic):

• $y^2=23 x^6+46 x^5+78 x^4+4 x^3+21 x^2+64 x+24$
• $y^2=27 x^6+20 x^5+78 x^4+41 x^3+26 x^2+20 x+2$
• $y^2=10 x^6+x^5+76 x^4+67 x^3+62 x^2+26 x+5$
• $y^2=8 x^6+33 x^5+21 x^4+57 x^3+29 x^2+2 x+70$
• $y^2=52 x^6+27 x^5+6 x^4+9 x^3+15 x^2+9 x+7$
• $y^2=67 x^6+11 x^5+5 x^4+78 x^3+31 x^2+70 x+20$
• $y^2=60 x^6+29 x^5+26 x^4+33 x^3+42 x^2+75 x+4$
• $y^2=74 x^6+23 x^5+62 x^4+37 x^3+44 x^2+16 x+23$
• $y^2=19 x^6+36 x^5+64 x^4+34 x^3+26 x^2+14 x+17$
• $y^2=32 x^6+61 x^5+41 x^4+8 x^3+56 x^2+59 x+7$
• $y^2=30 x^6+67 x^5+57 x^4+5 x^3+19 x^2+18 x+29$
• $y^2=50 x^6+30 x^5+17 x^4+62 x^3+68 x^2+13 x+55$
• $y^2=66 x^6+7 x^5+14 x^4+25 x^3+69 x^2+2 x+67$
• $y^2=11 x^6+9 x^5+34 x^4+23 x^3+13 x^2+39 x+22$
• $y^2=30 x^6+68 x^5+6 x^4+71 x^3+44 x^2+x+59$
• $y^2=51 x^6+18 x^5+18 x^4+31 x^3+28 x^2+19 x+35$
• $y^2=48 x^6+57 x^5+20 x^4+5 x^3+52 x^2+73 x+51$
• $y^2=57 x^6+65 x^5+67 x^4+11 x^3+76 x^2+46 x+52$
• $y^2=75 x^6+49 x^5+31 x^4+70 x^3+7 x^2+20 x+18$
• $y^2=33 x^6+24 x^5+36 x^4+61 x^3+20 x^2+70 x+24$
• and

• $y^2=12 x^6+14 x^5+24 x^4+35 x^3+37 x^2+43 x+38$
• $y^2=19 x^6+14 x^5+24 x^4+64 x^3+77 x^2+40 x+30$
• $y^2=40 x^6+54 x^5+48 x^4+38 x^3+41 x^2+52 x+9$
• $y^2=67 x^6+72 x^5+18 x^4+47 x^3+59 x^2+52$
• $y^2=57 x^6+38 x^5+11 x^4+58 x^3+49 x^2+24 x+14$
• $y^2=26 x^6+59 x^5+52 x^4+23 x^3+42 x^2+43 x+37$
• $y^2=51 x^6+27 x^4+65 x^2+18 x+18$
• $y^2=51 x^6+15 x^5+67 x^4+3 x^3+72 x^2+68 x+32$
• $y^2=39 x^6+42 x^5+47 x^4+55 x^3+7 x^2+61 x+13$
• $y^2=46 x^6+31 x^5+30 x^4+5 x^3+14 x^2+52 x+63$
• $y^2=46 x^6+10 x^5+x^4+6 x^3+58 x^2+73 x+60$
• $y^2=42 x^6+58 x^5+3 x^4+77 x^3+62 x^2+37 x+26$
• $y^2=75 x^6+61 x^5+36 x^4+9 x^3+x^2+39 x+68$
• $y^2=70 x^6+69 x^5+34 x^4+58 x^3+40 x^2+11 x+43$
• $y^2=48 x^6+50 x^5+78 x^4+62 x^3+41 x^2+39 x+65$
• $y^2=4 x^6+73 x^5+42 x^4+43 x^3+62 x^2+56 x+24$
• $y^2=53 x^6+50 x^5+26 x^4+56 x^3+45 x^2+5 x+41$
• $y^2=13 x^6+51 x^5+22 x^4+22 x^2+28 x+13$
• $y^2=29 x^6+51 x^5+24 x^4+76 x^3+76 x^2+30 x+15$
• $y^2=30 x^6+20 x^5+68 x^4+67 x^3+66 x^2+22 x+66$
• $y^2=9 x^6+51 x^5+62 x^4+54 x^3+75 x^2+52 x+16$
• $y^2=55 x^6+3 x^5+30 x^4+73 x^3+9 x^2+7 x+12$
• $y^2=5 x^6+14 x^5+61 x^4+50 x^3+21 x^2+74 x+52$
• $y^2=55 x^6+40 x^5+28 x^4+23 x^3+24 x^2+35 x+71$
• $y^2=22 x^6+45 x^5+67 x^4+66 x^3+6 x^2+69 x+73$
• $y^2=56 x^6+47 x^5+34 x^4+13 x^2+8 x+47$
• $y^2=13 x^6+17 x^5+17 x^4+16 x^3+59 x^2+9 x+2$
• $y^2=45 x^6+78 x^5+33 x^4+6 x^3+76 x^2+78 x+36$
• $y^2=42 x^6+18 x^5+52 x^4+51 x^3+35 x^2+64 x+76$
• $y^2=62 x^6+29 x^5+78 x^4+28 x^3+7 x^2+x+74$
• $y^2=44 x^6+13 x^5+45 x^4+33 x^3+15 x^2+48 x+42$
• $y^2=34 x^6+77 x^5+68 x^4+76 x^3+45 x^2+3 x+22$
• $y^2=77 x^6+74 x^5+7 x^4+71 x^3+53 x^2+31 x+18$
• $y^2=9 x^6+69 x^5+54 x^4+52 x^3+77 x^2+29 x+16$
• $y^2=76 x^6+33 x^5+14 x^4+39 x^3+77 x^2+7 x+40$
• $y^2=4 x^6+3 x^5+61 x^4+25 x^3+28 x^2+46 x+26$
• $y^2=55 x^6+77 x^4+43 x^3+22 x+13$
• $y^2=36 x^6+65 x^5+35 x^4+54 x^3+17 x^2+31 x+8$
• $y^2=61 x^6+14 x^5+24 x^4+70 x^3+34 x^2+39 x+62$
• $y^2=65 x^6+57 x^5+75 x^4+60 x^3+76 x^2+14 x+11$
• $y^2=66 x^6+67 x^5+44 x^4+40 x^3+51 x+16$
• $y^2=41 x^6+66 x^5+7 x^4+63 x^3+73 x^2+25 x+55$
• $y^2=65 x^6+78 x^5+15 x^4+15 x^2+x+65$
• $y^2=36 x^6+9 x^5+50 x^4+75 x^3+11 x^2+5 x+73$
• $y^2=4 x^6+37 x^5+33 x^4+54 x^3+20 x^2+64 x+62$
• $y^2=26 x^6+47 x^5+16 x^4+63 x^2+68 x+72$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79^{4}}$.

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is \(\Q(i, \sqrt{14})\).

Endomorphism algebra over $\overline{\F}_{79}$

The base change of $A$ to $\F_{79^{4}}$ is 1.38950081.gny^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-14}) \)$)$

Remainder of endomorphism lattice by field

• Endomorphism algebra over $\F_{79^{2}}$

  The base change of $A$ to $\F_{79^{2}}$ is the simple isogeny class 2.6241.a_gny and its endomorphism algebra is \(\Q(i, \sqrt{14})\).

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.ay_lc	$2$	(not in LMFDB)
2.79.a_afa	$8$	(not in LMFDB)
2.79.a_fa	$8$	(not in LMFDB)