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Properties

Label 12.36.2.b.1
Level $12$
Index $36$
Genus $2$
Analytic rank $0$
Cusps $4$
$\Q$-cusps $4$

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Invariants

Level: $12$ $\SL_2$-level: $12$ Newform level: $36$
Index: $36$ $\PSL_2$-index:$36$
Genus: $2 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps: $4$ (all of which are rational) Cusp widths $6^{2}\cdot12^{2}$ Cusp orbits $1^{4}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $0$
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 12B2
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 12.36.2.1

Level structure

$\GL_2(\Z/12\Z)$-generators: $\begin{bmatrix}5&10\\4&7\end{bmatrix}$, $\begin{bmatrix}9&2\\8&9\end{bmatrix}$, $\begin{bmatrix}9&4\\4&3\end{bmatrix}$, $\begin{bmatrix}11&6\\0&5\end{bmatrix}$, $\begin{bmatrix}11&8\\4&11\end{bmatrix}$
$\GL_2(\Z/12\Z)$-subgroup: $C_2^3\times \SD_{16}$
Contains $-I$: yes
Quadratic refinements: 12.72.2-12.b.1.1, 12.72.2-12.b.1.2, 12.72.2-12.b.1.3, 12.72.2-12.b.1.4, 12.72.2-12.b.1.5, 12.72.2-12.b.1.6, 12.72.2-12.b.1.7, 12.72.2-12.b.1.8, 12.72.2-12.b.1.9, 12.72.2-12.b.1.10, 12.72.2-12.b.1.11, 12.72.2-12.b.1.12, 24.72.2-12.b.1.1, 24.72.2-12.b.1.2, 24.72.2-12.b.1.3, 24.72.2-12.b.1.4, 24.72.2-12.b.1.5, 24.72.2-12.b.1.6, 24.72.2-12.b.1.7, 24.72.2-12.b.1.8, 24.72.2-12.b.1.9, 24.72.2-12.b.1.10, 24.72.2-12.b.1.11, 24.72.2-12.b.1.12, 24.72.2-12.b.1.13, 24.72.2-12.b.1.14, 24.72.2-12.b.1.15, 24.72.2-12.b.1.16, 24.72.2-12.b.1.17, 24.72.2-12.b.1.18, 24.72.2-12.b.1.19, 24.72.2-12.b.1.20, 24.72.2-12.b.1.21, 24.72.2-12.b.1.22, 24.72.2-12.b.1.23, 24.72.2-12.b.1.24, 24.72.2-12.b.1.25, 24.72.2-12.b.1.26, 24.72.2-12.b.1.27, 24.72.2-12.b.1.28, 24.72.2-12.b.1.29, 24.72.2-12.b.1.30, 24.72.2-12.b.1.31, 24.72.2-12.b.1.32, 24.72.2-12.b.1.33, 24.72.2-12.b.1.34, 24.72.2-12.b.1.35, 24.72.2-12.b.1.36, 24.72.2-12.b.1.37, 24.72.2-12.b.1.38, 24.72.2-12.b.1.39, 24.72.2-12.b.1.40, 24.72.2-12.b.1.41, 24.72.2-12.b.1.42, 24.72.2-12.b.1.43, 24.72.2-12.b.1.44, 60.72.2-12.b.1.1, 60.72.2-12.b.1.2, 60.72.2-12.b.1.3, 60.72.2-12.b.1.4, 60.72.2-12.b.1.5, 60.72.2-12.b.1.6, 60.72.2-12.b.1.7, 60.72.2-12.b.1.8, 60.72.2-12.b.1.9, 60.72.2-12.b.1.10, 60.72.2-12.b.1.11, 60.72.2-12.b.1.12, 84.72.2-12.b.1.1, 84.72.2-12.b.1.2, 84.72.2-12.b.1.3, 84.72.2-12.b.1.4, 84.72.2-12.b.1.5, 84.72.2-12.b.1.6, 84.72.2-12.b.1.7, 84.72.2-12.b.1.8, 84.72.2-12.b.1.9, 84.72.2-12.b.1.10, 84.72.2-12.b.1.11, 84.72.2-12.b.1.12, 120.72.2-12.b.1.1, 120.72.2-12.b.1.2, 120.72.2-12.b.1.3, 120.72.2-12.b.1.4, 120.72.2-12.b.1.5, 120.72.2-12.b.1.6, 120.72.2-12.b.1.7, 120.72.2-12.b.1.8, 120.72.2-12.b.1.9, 120.72.2-12.b.1.10, 120.72.2-12.b.1.11, 120.72.2-12.b.1.12, 120.72.2-12.b.1.13, 120.72.2-12.b.1.14, 120.72.2-12.b.1.15, 120.72.2-12.b.1.16, 120.72.2-12.b.1.17, 120.72.2-12.b.1.18, 120.72.2-12.b.1.19, 120.72.2-12.b.1.20, 120.72.2-12.b.1.21, 120.72.2-12.b.1.22, 120.72.2-12.b.1.23, 120.72.2-12.b.1.24, 120.72.2-12.b.1.25, 120.72.2-12.b.1.26, 120.72.2-12.b.1.27, 120.72.2-12.b.1.28, 120.72.2-12.b.1.29, 120.72.2-12.b.1.30, 120.72.2-12.b.1.31, 120.72.2-12.b.1.32, 120.72.2-12.b.1.33, 120.72.2-12.b.1.34, 120.72.2-12.b.1.35, 120.72.2-12.b.1.36, 120.72.2-12.b.1.37, 120.72.2-12.b.1.38, 120.72.2-12.b.1.39, 120.72.2-12.b.1.40, 120.72.2-12.b.1.41, 120.72.2-12.b.1.42, 120.72.2-12.b.1.43, 120.72.2-12.b.1.44, 132.72.2-12.b.1.1, 132.72.2-12.b.1.2, 132.72.2-12.b.1.3, 132.72.2-12.b.1.4, 132.72.2-12.b.1.5, 132.72.2-12.b.1.6, 132.72.2-12.b.1.7, 132.72.2-12.b.1.8, 132.72.2-12.b.1.9, 132.72.2-12.b.1.10, 132.72.2-12.b.1.11, 132.72.2-12.b.1.12, 156.72.2-12.b.1.1, 156.72.2-12.b.1.2, 156.72.2-12.b.1.3, 156.72.2-12.b.1.4, 156.72.2-12.b.1.5, 156.72.2-12.b.1.6, 156.72.2-12.b.1.7, 156.72.2-12.b.1.8, 156.72.2-12.b.1.9, 156.72.2-12.b.1.10, 156.72.2-12.b.1.11, 156.72.2-12.b.1.12, 168.72.2-12.b.1.1, 168.72.2-12.b.1.2, 168.72.2-12.b.1.3, 168.72.2-12.b.1.4, 168.72.2-12.b.1.5, 168.72.2-12.b.1.6, 168.72.2-12.b.1.7, 168.72.2-12.b.1.8, 168.72.2-12.b.1.9, 168.72.2-12.b.1.10, 168.72.2-12.b.1.11, 168.72.2-12.b.1.12, 168.72.2-12.b.1.13, 168.72.2-12.b.1.14, 168.72.2-12.b.1.15, 168.72.2-12.b.1.16, 168.72.2-12.b.1.17, 168.72.2-12.b.1.18, 168.72.2-12.b.1.19, 168.72.2-12.b.1.20, 168.72.2-12.b.1.21, 168.72.2-12.b.1.22, 168.72.2-12.b.1.23, 168.72.2-12.b.1.24, 168.72.2-12.b.1.25, 168.72.2-12.b.1.26, 168.72.2-12.b.1.27, 168.72.2-12.b.1.28, 168.72.2-12.b.1.29, 168.72.2-12.b.1.30, 168.72.2-12.b.1.31, 168.72.2-12.b.1.32, 168.72.2-12.b.1.33, 168.72.2-12.b.1.34, 168.72.2-12.b.1.35, 168.72.2-12.b.1.36, 168.72.2-12.b.1.37, 168.72.2-12.b.1.38, 168.72.2-12.b.1.39, 168.72.2-12.b.1.40, 168.72.2-12.b.1.41, 168.72.2-12.b.1.42, 168.72.2-12.b.1.43, 168.72.2-12.b.1.44, 204.72.2-12.b.1.1, 204.72.2-12.b.1.2, 204.72.2-12.b.1.3, 204.72.2-12.b.1.4, 204.72.2-12.b.1.5, 204.72.2-12.b.1.6, 204.72.2-12.b.1.7, 204.72.2-12.b.1.8, 204.72.2-12.b.1.9, 204.72.2-12.b.1.10, 204.72.2-12.b.1.11, 204.72.2-12.b.1.12, 228.72.2-12.b.1.1, 228.72.2-12.b.1.2, 228.72.2-12.b.1.3, 228.72.2-12.b.1.4, 228.72.2-12.b.1.5, 228.72.2-12.b.1.6, 228.72.2-12.b.1.7, 228.72.2-12.b.1.8, 228.72.2-12.b.1.9, 228.72.2-12.b.1.10, 228.72.2-12.b.1.11, 228.72.2-12.b.1.12, 264.72.2-12.b.1.1, 264.72.2-12.b.1.2, 264.72.2-12.b.1.3, 264.72.2-12.b.1.4, 264.72.2-12.b.1.5, 264.72.2-12.b.1.6, 264.72.2-12.b.1.7, 264.72.2-12.b.1.8, 264.72.2-12.b.1.9, 264.72.2-12.b.1.10, 264.72.2-12.b.1.11, 264.72.2-12.b.1.12, 264.72.2-12.b.1.13, 264.72.2-12.b.1.14, 264.72.2-12.b.1.15, 264.72.2-12.b.1.16, 264.72.2-12.b.1.17, 264.72.2-12.b.1.18, 264.72.2-12.b.1.19, 264.72.2-12.b.1.20, 264.72.2-12.b.1.21, 264.72.2-12.b.1.22, 264.72.2-12.b.1.23, 264.72.2-12.b.1.24, 264.72.2-12.b.1.25, 264.72.2-12.b.1.26, 264.72.2-12.b.1.27, 264.72.2-12.b.1.28, 264.72.2-12.b.1.29, 264.72.2-12.b.1.30, 264.72.2-12.b.1.31, 264.72.2-12.b.1.32, 264.72.2-12.b.1.33, 264.72.2-12.b.1.34, 264.72.2-12.b.1.35, 264.72.2-12.b.1.36, 264.72.2-12.b.1.37, 264.72.2-12.b.1.38, 264.72.2-12.b.1.39, 264.72.2-12.b.1.40, 264.72.2-12.b.1.41, 264.72.2-12.b.1.42, 264.72.2-12.b.1.43, 264.72.2-12.b.1.44, 276.72.2-12.b.1.1, 276.72.2-12.b.1.2, 276.72.2-12.b.1.3, 276.72.2-12.b.1.4, 276.72.2-12.b.1.5, 276.72.2-12.b.1.6, 276.72.2-12.b.1.7, 276.72.2-12.b.1.8, 276.72.2-12.b.1.9, 276.72.2-12.b.1.10, 276.72.2-12.b.1.11, 276.72.2-12.b.1.12, 312.72.2-12.b.1.1, 312.72.2-12.b.1.2, 312.72.2-12.b.1.3, 312.72.2-12.b.1.4, 312.72.2-12.b.1.5, 312.72.2-12.b.1.6, 312.72.2-12.b.1.7, 312.72.2-12.b.1.8, 312.72.2-12.b.1.9, 312.72.2-12.b.1.10, 312.72.2-12.b.1.11, 312.72.2-12.b.1.12, 312.72.2-12.b.1.13, 312.72.2-12.b.1.14, 312.72.2-12.b.1.15, 312.72.2-12.b.1.16, 312.72.2-12.b.1.17, 312.72.2-12.b.1.18, 312.72.2-12.b.1.19, 312.72.2-12.b.1.20, 312.72.2-12.b.1.21, 312.72.2-12.b.1.22, 312.72.2-12.b.1.23, 312.72.2-12.b.1.24, 312.72.2-12.b.1.25, 312.72.2-12.b.1.26, 312.72.2-12.b.1.27, 312.72.2-12.b.1.28, 312.72.2-12.b.1.29, 312.72.2-12.b.1.30, 312.72.2-12.b.1.31, 312.72.2-12.b.1.32, 312.72.2-12.b.1.33, 312.72.2-12.b.1.34, 312.72.2-12.b.1.35, 312.72.2-12.b.1.36, 312.72.2-12.b.1.37, 312.72.2-12.b.1.38, 312.72.2-12.b.1.39, 312.72.2-12.b.1.40, 312.72.2-12.b.1.41, 312.72.2-12.b.1.42, 312.72.2-12.b.1.43, 312.72.2-12.b.1.44
Cyclic 12-isogeny field degree: $4$
Cyclic 12-torsion field degree: $16$
Full 12-torsion field degree: $128$

Jacobian

Conductor: $2^{4}\cdot3^{4}$
Simple: no
Squarefree: no
Decomposition: $1^{2}$
Newforms: 36.2.a.a$^{2}$

Models

Embedded model Embedded model in $\mathbb{P}^{3}$

$ 0 $ $=$ $ x^{2} z - y^{2} w + z^{2} w $
$=$ $x y w - 4 w^{3}$
$=$ $x y z - 4 z w^{2}$
$=$ $x y^{2} - 4 y w^{2}$
$=$$\cdots$
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Singular plane model Singular plane model

$ 0 $ $=$ $ x^{4} - x^{2} y^{2} - 2 y z^{3} $
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Weierstrass model Weierstrass model

$ y^{2} $ $=$ $ x^{6} + 1 $
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Rational points

This modular curve has 4 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.

Embedded model
$(1:0:0:0)$, $(0:-1:1:0)$, $(0:0:1:0)$, $(0:1:1:0)$

Maps between models of this curve

Birational map from embedded model to plane model:

$\displaystyle X$ $=$ $\displaystyle y$
$\displaystyle Y$ $=$ $\displaystyle z$
$\displaystyle Z$ $=$ $\displaystyle 2w$

Birational map from embedded model to Weierstrass model:

$\displaystyle X$ $=$ $\displaystyle \frac{1}{2}y$
$\displaystyle Y$ $=$ $\displaystyle \frac{1}{8}y^{2}z+w^{3}$
$\displaystyle Z$ $=$ $\displaystyle w$

Maps to other modular curves

$j$-invariant map of degree 36 from the embedded model of this modular curve to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle \frac{256x^{4}w^{4}+256y^{2}w^{6}+z^{8}+48z^{5}w^{3}+512z^{2}w^{6}}{w^{6}z^{2}}$

Modular covers

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Cover information

Click on a modular curve in the diagram to see information about it.
See a full page version of the diagram

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_{\mathrm{ns}}^+(3)$ $3$ $12$ $12$ $0$ $0$ full Jacobian
$X_{\pm1}(2,4)$ $4$ $3$ $3$ $0$ $0$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_{\pm1}(2,4)$ $4$ $3$ $3$ $0$ $0$ full Jacobian
6.18.1.a.1 $6$ $2$ $2$ $1$ $0$ $1$
12.18.0.k.1 $12$ $2$ $2$ $0$ $0$ full Jacobian
12.18.1.c.1 $12$ $2$ $2$ $1$ $0$ $1$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
12.72.3.b.1 $12$ $2$ $2$ $3$ $0$ $1$
12.72.3.d.1 $12$ $2$ $2$ $3$ $0$ $1$
12.72.3.k.1 $12$ $2$ $2$ $3$ $0$ $1$
12.72.3.l.1 $12$ $2$ $2$ $3$ $0$ $1$
12.72.4.b.1 $12$ $2$ $2$ $4$ $0$ $1^{2}$
12.72.4.e.1 $12$ $2$ $2$ $4$ $0$ $1^{2}$
12.72.4.h.1 $12$ $2$ $2$ $4$ $0$ $1^{2}$
12.72.4.k.1 $12$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.3.e.1 $24$ $2$ $2$ $3$ $1$ $1$
24.72.3.k.1 $24$ $2$ $2$ $3$ $0$ $1$
24.72.3.be.1 $24$ $2$ $2$ $3$ $0$ $1$
24.72.3.bh.1 $24$ $2$ $2$ $3$ $0$ $1$
24.72.4.c.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.h.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.m.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.4.n.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.q.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.4.r.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.4.s.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.s.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.t.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.t.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.u.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.u.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.v.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.v.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.w.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.w.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.x.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.x.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.y.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.y.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.z.1 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.z.2 $24$ $2$ $2$ $4$ $0$ $2$
24.72.4.be.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.4.bl.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.cc.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.cd.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.4.cg.1 $24$ $2$ $2$ $4$ $1$ $1^{2}$
24.72.4.ch.1 $24$ $2$ $2$ $4$ $0$ $1^{2}$
24.72.5.c.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
24.72.5.d.1 $24$ $2$ $2$ $5$ $0$ $1^{3}$
24.72.5.g.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
24.72.5.h.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
24.72.5.k.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
24.72.5.l.1 $24$ $2$ $2$ $5$ $0$ $1^{3}$
24.72.5.o.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
24.72.5.p.1 $24$ $2$ $2$ $5$ $1$ $1^{3}$
36.108.8.b.1 $36$ $3$ $3$ $8$ $1$ $1^{6}$
36.324.22.f.1 $36$ $9$ $9$ $22$ $5$ $1^{18}\cdot2$
60.72.3.o.1 $60$ $2$ $2$ $3$ $1$ $1$
60.72.3.p.1 $60$ $2$ $2$ $3$ $0$ $1$
60.72.3.w.1 $60$ $2$ $2$ $3$ $0$ $1$
60.72.3.x.1 $60$ $2$ $2$ $3$ $1$ $1$
60.72.4.c.1 $60$ $2$ $2$ $4$ $0$ $1^{2}$
60.72.4.f.1 $60$ $2$ $2$ $4$ $0$ $1^{2}$
60.72.4.m.1 $60$ $2$ $2$ $4$ $1$ $1^{2}$
60.72.4.p.1 $60$ $2$ $2$ $4$ $1$ $1^{2}$
60.180.14.b.1 $60$ $5$ $5$ $14$ $5$ $1^{12}$
60.216.15.b.1 $60$ $6$ $6$ $15$ $0$ $1^{13}$
60.360.27.cr.1 $60$ $10$ $10$ $27$ $9$ $1^{25}$
84.72.3.k.1 $84$ $2$ $2$ $3$ $?$ not computed
84.72.3.l.1 $84$ $2$ $2$ $3$ $?$ not computed
84.72.3.s.1 $84$ $2$ $2$ $3$ $?$ not computed
84.72.3.t.1 $84$ $2$ $2$ $3$ $?$ not computed
84.72.4.c.1 $84$ $2$ $2$ $4$ $?$ not computed
84.72.4.f.1 $84$ $2$ $2$ $4$ $?$ not computed
84.72.4.m.1 $84$ $2$ $2$ $4$ $?$ not computed
84.72.4.p.1 $84$ $2$ $2$ $4$ $?$ not computed
84.288.21.b.1 $84$ $8$ $8$ $21$ $?$ not computed
120.72.3.bi.1 $120$ $2$ $2$ $3$ $?$ not computed
120.72.3.bl.1 $120$ $2$ $2$ $3$ $?$ not computed
120.72.3.cg.1 $120$ $2$ $2$ $3$ $?$ not computed
120.72.3.cj.1 $120$ $2$ $2$ $3$ $?$ not computed
120.72.4.e.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.l.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bc.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bd.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bg.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bh.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bi.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bi.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bj.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bj.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bk.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bk.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bl.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bl.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bm.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bm.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bn.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bn.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bo.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bo.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bp.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bp.2 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.bu.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.cb.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.eo.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.ep.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.es.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.4.et.1 $120$ $2$ $2$ $4$ $?$ not computed
120.72.5.c.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.d.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.g.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.h.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.k.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.l.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.o.1 $120$ $2$ $2$ $5$ $?$ not computed
120.72.5.p.1 $120$ $2$ $2$ $5$ $?$ not computed
132.72.3.k.1 $132$ $2$ $2$ $3$ $?$ not computed
132.72.3.l.1 $132$ $2$ $2$ $3$ $?$ not computed
132.72.3.s.1 $132$ $2$ $2$ $3$ $?$ not computed
132.72.3.t.1 $132$ $2$ $2$ $3$ $?$ not computed
132.72.4.c.1 $132$ $2$ $2$ $4$ $?$ not computed
132.72.4.f.1 $132$ $2$ $2$ $4$ $?$ not computed
132.72.4.m.1 $132$ $2$ $2$ $4$ $?$ not computed
132.72.4.p.1 $132$ $2$ $2$ $4$ $?$ not computed
156.72.3.k.1 $156$ $2$ $2$ $3$ $?$ not computed
156.72.3.l.1 $156$ $2$ $2$ $3$ $?$ not computed
156.72.3.s.1 $156$ $2$ $2$ $3$ $?$ not computed
156.72.3.t.1 $156$ $2$ $2$ $3$ $?$ not computed
156.72.4.c.1 $156$ $2$ $2$ $4$ $?$ not computed
156.72.4.f.1 $156$ $2$ $2$ $4$ $?$ not computed
156.72.4.m.1 $156$ $2$ $2$ $4$ $?$ not computed
156.72.4.p.1 $156$ $2$ $2$ $4$ $?$ not computed
168.72.3.be.1 $168$ $2$ $2$ $3$ $?$ not computed
168.72.3.bh.1 $168$ $2$ $2$ $3$ $?$ not computed
168.72.3.cc.1 $168$ $2$ $2$ $3$ $?$ not computed
168.72.3.cf.1 $168$ $2$ $2$ $3$ $?$ not computed
168.72.4.e.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.l.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bc.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bd.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bg.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bh.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bi.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bi.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bj.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bj.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bk.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bk.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bl.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bl.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bm.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bm.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bn.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bn.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bo.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bo.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bp.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bp.2 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.bu.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.cb.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.eo.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.ep.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.es.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.4.et.1 $168$ $2$ $2$ $4$ $?$ not computed
168.72.5.c.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.d.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.g.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.h.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.k.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.l.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.o.1 $168$ $2$ $2$ $5$ $?$ not computed
168.72.5.p.1 $168$ $2$ $2$ $5$ $?$ not computed
204.72.3.k.1 $204$ $2$ $2$ $3$ $?$ not computed
204.72.3.l.1 $204$ $2$ $2$ $3$ $?$ not computed
204.72.3.s.1 $204$ $2$ $2$ $3$ $?$ not computed
204.72.3.t.1 $204$ $2$ $2$ $3$ $?$ not computed
204.72.4.c.1 $204$ $2$ $2$ $4$ $?$ not computed
204.72.4.f.1 $204$ $2$ $2$ $4$ $?$ not computed
204.72.4.m.1 $204$ $2$ $2$ $4$ $?$ not computed
204.72.4.p.1 $204$ $2$ $2$ $4$ $?$ not computed
228.72.3.k.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.l.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.s.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.3.t.1 $228$ $2$ $2$ $3$ $?$ not computed
228.72.4.c.1 $228$ $2$ $2$ $4$ $?$ not computed
228.72.4.f.1 $228$ $2$ $2$ $4$ $?$ not computed
228.72.4.m.1 $228$ $2$ $2$ $4$ $?$ not computed
228.72.4.p.1 $228$ $2$ $2$ $4$ $?$ not computed
264.72.3.be.1 $264$ $2$ $2$ $3$ $?$ not computed
264.72.3.bh.1 $264$ $2$ $2$ $3$ $?$ not computed
264.72.3.cc.1 $264$ $2$ $2$ $3$ $?$ not computed
264.72.3.cf.1 $264$ $2$ $2$ $3$ $?$ not computed
264.72.4.e.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.l.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bc.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bd.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bg.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bh.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bi.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bi.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bj.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bj.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bk.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bk.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bl.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bl.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bm.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bm.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bn.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bn.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bo.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bo.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bp.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bp.2 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.bu.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.cb.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.eo.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.ep.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.es.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.4.et.1 $264$ $2$ $2$ $4$ $?$ not computed
264.72.5.c.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.d.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.g.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.h.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.k.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.l.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.o.1 $264$ $2$ $2$ $5$ $?$ not computed
264.72.5.p.1 $264$ $2$ $2$ $5$ $?$ not computed
276.72.3.k.1 $276$ $2$ $2$ $3$ $?$ not computed
276.72.3.l.1 $276$ $2$ $2$ $3$ $?$ not computed
276.72.3.s.1 $276$ $2$ $2$ $3$ $?$ not computed
276.72.3.t.1 $276$ $2$ $2$ $3$ $?$ not computed
276.72.4.c.1 $276$ $2$ $2$ $4$ $?$ not computed
276.72.4.f.1 $276$ $2$ $2$ $4$ $?$ not computed
276.72.4.m.1 $276$ $2$ $2$ $4$ $?$ not computed
276.72.4.p.1 $276$ $2$ $2$ $4$ $?$ not computed
312.72.3.be.1 $312$ $2$ $2$ $3$ $?$ not computed
312.72.3.bh.1 $312$ $2$ $2$ $3$ $?$ not computed
312.72.3.cc.1 $312$ $2$ $2$ $3$ $?$ not computed
312.72.3.cf.1 $312$ $2$ $2$ $3$ $?$ not computed
312.72.4.e.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.l.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bc.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bd.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bg.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bh.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bi.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bi.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bj.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bj.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bk.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bk.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bl.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bl.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bm.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bm.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bn.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bn.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bo.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bo.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bp.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bp.2 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.bu.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.cb.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.eo.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.ep.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.es.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.4.et.1 $312$ $2$ $2$ $4$ $?$ not computed
312.72.5.c.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.d.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.g.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.h.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.k.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.l.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.o.1 $312$ $2$ $2$ $5$ $?$ not computed
312.72.5.p.1 $312$ $2$ $2$ $5$ $?$ not computed