Abelian variety isogeny class 2.37.o_ee over $\F_{37}$

• Label: 2.37.o_ee
• Base field: $\F_{37}$
• 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:	$\F_{37}$
Dimension:	$2$
L-polynomial:	$1 + 14 x + 108 x^{2} + 518 x^{3} + 1369 x^{4}$
Frobenius angles:	$\pm0.582746945236$, $\pm0.851937754380$
Angle rank:	$2$ (numerical)
Number field:	4.0.302400.2
Galois group:	$D_{4}$
Jacobians:	$36$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2010$	$1901460$	$2553747210$	$3511350123600$	$4808905667870250$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$1390$	$50416$	$1873558$	$69348592$	$2565822670$	$94930667716$	$3512484416158$	$129961744734292$	$4808584262045950$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=33 x^6+10 x^5+3 x^4+11 x^3+19 x^2+14 x+4$
• $y^2=3 x^6+17 x^5+28 x^4+7 x^3+28 x^2+27 x+25$
• $y^2=36 x^6+12 x^5+27 x^4+11 x^3+11 x^2+29 x+16$
• $y^2=9 x^6+25 x^5+12 x^4+14 x^3+10 x^2+17 x+23$
• $y^2=22 x^6+23 x^5+13 x^4+19 x^3+6 x^2+17 x+2$
• $y^2=4 x^6+3 x^5+31 x^4+34 x^3+26 x^2+27 x+30$
• $y^2=10 x^6+x^5+13 x^4+31 x^3+27 x^2+30 x+3$
• $y^2=21 x^6+29 x^5+6 x^4+17 x^3+14 x^2+28 x+21$
• $y^2=26 x^6+12 x^5+26 x^4+21 x^3+23 x^2+24 x+12$
• $y^2=4 x^6+33 x^5+28 x^4+32 x^3+29 x^2+4 x+9$
• $y^2=9 x^6+35 x^5+19 x^4+20 x^3+35 x^2+13 x$
• $y^2=13 x^6+5 x^5+11 x^4+3 x^3+12 x^2+15 x+34$
• $y^2=9 x^6+20 x^5+15 x^4+31 x^3+2 x^2+9 x+34$
• $y^2=3 x^6+19 x^5+24 x^4+14 x^3+17 x^2+18 x+2$
• $y^2=34 x^6+6 x^5+11 x^3+5 x+34$
• $y^2=25 x^6+13 x^5+16 x^4+29 x^3+2 x^2+29 x+4$
• $y^2=28 x^6+33 x^5+x^4+26 x^3+18 x^2+10 x+11$
• $y^2=30 x^6+20 x^5+6 x^4+33 x^3+24 x^2+6 x+26$
• $y^2=25 x^6+12 x^5+11 x^4+33 x^3+28 x^2+31 x+1$
• $y^2=30 x^6+10 x^5+x^3+17 x^2+10 x+4$
• and

• $y^2=36 x^6+22 x^5+26 x^3+8 x^2+25 x+11$
• $y^2=13 x^6+35 x^5+22 x^4+19 x^3+7 x^2+9 x+16$
• $y^2=7 x^6+17 x^5+31 x^4+2 x^3+21 x^2+9 x+21$
• $y^2=26 x^6+29 x^5+32 x^4+30 x^3+6 x^2+34 x+28$
• $y^2=24 x^6+31 x^5+12 x^4+24 x^3+26 x^2+6$
• $y^2=34 x^6+34 x^5+11 x^4+16 x^3+17 x^2+9 x+10$
• $y^2=34 x^6+5 x^5+27 x^4+21 x^3+31 x^2+2 x+35$
• $y^2=3 x^6+19 x^5+21 x^4+11 x^3+24 x^2+32 x+28$
• $y^2=30 x^6+3 x^5+21 x^4+8 x^3+5 x+34$
• $y^2=14 x^6+34 x^5+6 x^4+x^3+24 x^2+27 x+34$
• $y^2=11 x^6+15 x^5+6 x^4+36 x^3+30 x^2+35 x+33$
• $y^2=16 x^6+30 x^5+14 x^4+18 x^3+24 x^2+16 x$
• $y^2=7 x^6+19 x^5+21 x^4+24 x^3+32 x^2+17 x+21$
• $y^2=22 x^6+5 x^5+8 x^4+36 x^3+10$
• $y^2=24 x^6+28 x^5+16 x^4+20 x^3+16 x^2+27 x+20$
• $y^2=12 x^6+5 x^5+10 x^4+24 x^3+15 x^2+20 x+21$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{37}$.

Endomorphism algebra over $\F_{37}$

The endomorphism algebra of this simple isogeny class is 4.0.302400.2.

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
2.37.ao_ee	$2$	(not in LMFDB)