Properties

Label 24.72.4.ch.1
Level $24$
Index $72$
Genus $4$
Analytic rank $0$
Cusps $6$
$\Q$-cusps $4$

Related objects

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Invariants

Level: $24$ $\SL_2$-level: $24$ Newform level: $144$
Index: $72$ $\PSL_2$-index:$72$
Genus: $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (of which $4$ are rational) Cusp widths $6^{4}\cdot24^{2}$ Cusp orbits $1^{4}\cdot2$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $0$
$\Q$-gonality: $3$
$\overline{\Q}$-gonality: $3$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24D4
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 24.72.4.6

Level structure

$\GL_2(\Z/24\Z)$-generators: $\begin{bmatrix}1&6\\0&23\end{bmatrix}$, $\begin{bmatrix}5&0\\0&1\end{bmatrix}$, $\begin{bmatrix}15&2\\16&3\end{bmatrix}$, $\begin{bmatrix}17&22\\8&5\end{bmatrix}$, $\begin{bmatrix}23&16\\8&17\end{bmatrix}$, $\begin{bmatrix}23&20\\8&7\end{bmatrix}$, $\begin{bmatrix}23&22\\16&19\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 24.144.4-24.ch.1.1, 24.144.4-24.ch.1.2, 24.144.4-24.ch.1.3, 24.144.4-24.ch.1.4, 24.144.4-24.ch.1.5, 24.144.4-24.ch.1.6, 24.144.4-24.ch.1.7, 24.144.4-24.ch.1.8, 24.144.4-24.ch.1.9, 24.144.4-24.ch.1.10, 24.144.4-24.ch.1.11, 24.144.4-24.ch.1.12, 24.144.4-24.ch.1.13, 24.144.4-24.ch.1.14, 24.144.4-24.ch.1.15, 24.144.4-24.ch.1.16, 24.144.4-24.ch.1.17, 24.144.4-24.ch.1.18, 24.144.4-24.ch.1.19, 24.144.4-24.ch.1.20, 24.144.4-24.ch.1.21, 24.144.4-24.ch.1.22, 24.144.4-24.ch.1.23, 24.144.4-24.ch.1.24, 24.144.4-24.ch.1.25, 24.144.4-24.ch.1.26, 24.144.4-24.ch.1.27, 24.144.4-24.ch.1.28, 24.144.4-24.ch.1.29, 24.144.4-24.ch.1.30, 24.144.4-24.ch.1.31, 24.144.4-24.ch.1.32, 24.144.4-24.ch.1.33, 24.144.4-24.ch.1.34, 24.144.4-24.ch.1.35, 24.144.4-24.ch.1.36, 24.144.4-24.ch.1.37, 24.144.4-24.ch.1.38, 24.144.4-24.ch.1.39, 24.144.4-24.ch.1.40, 24.144.4-24.ch.1.41, 24.144.4-24.ch.1.42, 24.144.4-24.ch.1.43, 24.144.4-24.ch.1.44, 24.144.4-24.ch.1.45, 24.144.4-24.ch.1.46, 24.144.4-24.ch.1.47, 24.144.4-24.ch.1.48, 48.144.4-24.ch.1.1, 48.144.4-24.ch.1.2, 48.144.4-24.ch.1.3, 48.144.4-24.ch.1.4, 48.144.4-24.ch.1.5, 48.144.4-24.ch.1.6, 48.144.4-24.ch.1.7, 48.144.4-24.ch.1.8, 48.144.4-24.ch.1.9, 48.144.4-24.ch.1.10, 48.144.4-24.ch.1.11, 48.144.4-24.ch.1.12, 48.144.4-24.ch.1.13, 48.144.4-24.ch.1.14, 48.144.4-24.ch.1.15, 48.144.4-24.ch.1.16, 48.144.4-24.ch.1.17, 48.144.4-24.ch.1.18, 48.144.4-24.ch.1.19, 48.144.4-24.ch.1.20, 48.144.4-24.ch.1.21, 48.144.4-24.ch.1.22, 48.144.4-24.ch.1.23, 48.144.4-24.ch.1.24, 48.144.4-24.ch.1.25, 48.144.4-24.ch.1.26, 48.144.4-24.ch.1.27, 48.144.4-24.ch.1.28, 48.144.4-24.ch.1.29, 48.144.4-24.ch.1.30, 48.144.4-24.ch.1.31, 48.144.4-24.ch.1.32, 120.144.4-24.ch.1.1, 120.144.4-24.ch.1.2, 120.144.4-24.ch.1.3, 120.144.4-24.ch.1.4, 120.144.4-24.ch.1.5, 120.144.4-24.ch.1.6, 120.144.4-24.ch.1.7, 120.144.4-24.ch.1.8, 120.144.4-24.ch.1.9, 120.144.4-24.ch.1.10, 120.144.4-24.ch.1.11, 120.144.4-24.ch.1.12, 120.144.4-24.ch.1.13, 120.144.4-24.ch.1.14, 120.144.4-24.ch.1.15, 120.144.4-24.ch.1.16, 120.144.4-24.ch.1.17, 120.144.4-24.ch.1.18, 120.144.4-24.ch.1.19, 120.144.4-24.ch.1.20, 120.144.4-24.ch.1.21, 120.144.4-24.ch.1.22, 120.144.4-24.ch.1.23, 120.144.4-24.ch.1.24, 120.144.4-24.ch.1.25, 120.144.4-24.ch.1.26, 120.144.4-24.ch.1.27, 120.144.4-24.ch.1.28, 120.144.4-24.ch.1.29, 120.144.4-24.ch.1.30, 120.144.4-24.ch.1.31, 120.144.4-24.ch.1.32, 120.144.4-24.ch.1.33, 120.144.4-24.ch.1.34, 120.144.4-24.ch.1.35, 120.144.4-24.ch.1.36, 120.144.4-24.ch.1.37, 120.144.4-24.ch.1.38, 120.144.4-24.ch.1.39, 120.144.4-24.ch.1.40, 120.144.4-24.ch.1.41, 120.144.4-24.ch.1.42, 120.144.4-24.ch.1.43, 120.144.4-24.ch.1.44, 120.144.4-24.ch.1.45, 120.144.4-24.ch.1.46, 120.144.4-24.ch.1.47, 120.144.4-24.ch.1.48, 168.144.4-24.ch.1.1, 168.144.4-24.ch.1.2, 168.144.4-24.ch.1.3, 168.144.4-24.ch.1.4, 168.144.4-24.ch.1.5, 168.144.4-24.ch.1.6, 168.144.4-24.ch.1.7, 168.144.4-24.ch.1.8, 168.144.4-24.ch.1.9, 168.144.4-24.ch.1.10, 168.144.4-24.ch.1.11, 168.144.4-24.ch.1.12, 168.144.4-24.ch.1.13, 168.144.4-24.ch.1.14, 168.144.4-24.ch.1.15, 168.144.4-24.ch.1.16, 168.144.4-24.ch.1.17, 168.144.4-24.ch.1.18, 168.144.4-24.ch.1.19, 168.144.4-24.ch.1.20, 168.144.4-24.ch.1.21, 168.144.4-24.ch.1.22, 168.144.4-24.ch.1.23, 168.144.4-24.ch.1.24, 168.144.4-24.ch.1.25, 168.144.4-24.ch.1.26, 168.144.4-24.ch.1.27, 168.144.4-24.ch.1.28, 168.144.4-24.ch.1.29, 168.144.4-24.ch.1.30, 168.144.4-24.ch.1.31, 168.144.4-24.ch.1.32, 168.144.4-24.ch.1.33, 168.144.4-24.ch.1.34, 168.144.4-24.ch.1.35, 168.144.4-24.ch.1.36, 168.144.4-24.ch.1.37, 168.144.4-24.ch.1.38, 168.144.4-24.ch.1.39, 168.144.4-24.ch.1.40, 168.144.4-24.ch.1.41, 168.144.4-24.ch.1.42, 168.144.4-24.ch.1.43, 168.144.4-24.ch.1.44, 168.144.4-24.ch.1.45, 168.144.4-24.ch.1.46, 168.144.4-24.ch.1.47, 168.144.4-24.ch.1.48, 240.144.4-24.ch.1.1, 240.144.4-24.ch.1.2, 240.144.4-24.ch.1.3, 240.144.4-24.ch.1.4, 240.144.4-24.ch.1.5, 240.144.4-24.ch.1.6, 240.144.4-24.ch.1.7, 240.144.4-24.ch.1.8, 240.144.4-24.ch.1.9, 240.144.4-24.ch.1.10, 240.144.4-24.ch.1.11, 240.144.4-24.ch.1.12, 240.144.4-24.ch.1.13, 240.144.4-24.ch.1.14, 240.144.4-24.ch.1.15, 240.144.4-24.ch.1.16, 240.144.4-24.ch.1.17, 240.144.4-24.ch.1.18, 240.144.4-24.ch.1.19, 240.144.4-24.ch.1.20, 240.144.4-24.ch.1.21, 240.144.4-24.ch.1.22, 240.144.4-24.ch.1.23, 240.144.4-24.ch.1.24, 240.144.4-24.ch.1.25, 240.144.4-24.ch.1.26, 240.144.4-24.ch.1.27, 240.144.4-24.ch.1.28, 240.144.4-24.ch.1.29, 240.144.4-24.ch.1.30, 240.144.4-24.ch.1.31, 240.144.4-24.ch.1.32, 264.144.4-24.ch.1.1, 264.144.4-24.ch.1.2, 264.144.4-24.ch.1.3, 264.144.4-24.ch.1.4, 264.144.4-24.ch.1.5, 264.144.4-24.ch.1.6, 264.144.4-24.ch.1.7, 264.144.4-24.ch.1.8, 264.144.4-24.ch.1.9, 264.144.4-24.ch.1.10, 264.144.4-24.ch.1.11, 264.144.4-24.ch.1.12, 264.144.4-24.ch.1.13, 264.144.4-24.ch.1.14, 264.144.4-24.ch.1.15, 264.144.4-24.ch.1.16, 264.144.4-24.ch.1.17, 264.144.4-24.ch.1.18, 264.144.4-24.ch.1.19, 264.144.4-24.ch.1.20, 264.144.4-24.ch.1.21, 264.144.4-24.ch.1.22, 264.144.4-24.ch.1.23, 264.144.4-24.ch.1.24, 264.144.4-24.ch.1.25, 264.144.4-24.ch.1.26, 264.144.4-24.ch.1.27, 264.144.4-24.ch.1.28, 264.144.4-24.ch.1.29, 264.144.4-24.ch.1.30, 264.144.4-24.ch.1.31, 264.144.4-24.ch.1.32, 264.144.4-24.ch.1.33, 264.144.4-24.ch.1.34, 264.144.4-24.ch.1.35, 264.144.4-24.ch.1.36, 264.144.4-24.ch.1.37, 264.144.4-24.ch.1.38, 264.144.4-24.ch.1.39, 264.144.4-24.ch.1.40, 264.144.4-24.ch.1.41, 264.144.4-24.ch.1.42, 264.144.4-24.ch.1.43, 264.144.4-24.ch.1.44, 264.144.4-24.ch.1.45, 264.144.4-24.ch.1.46, 264.144.4-24.ch.1.47, 264.144.4-24.ch.1.48, 312.144.4-24.ch.1.1, 312.144.4-24.ch.1.2, 312.144.4-24.ch.1.3, 312.144.4-24.ch.1.4, 312.144.4-24.ch.1.5, 312.144.4-24.ch.1.6, 312.144.4-24.ch.1.7, 312.144.4-24.ch.1.8, 312.144.4-24.ch.1.9, 312.144.4-24.ch.1.10, 312.144.4-24.ch.1.11, 312.144.4-24.ch.1.12, 312.144.4-24.ch.1.13, 312.144.4-24.ch.1.14, 312.144.4-24.ch.1.15, 312.144.4-24.ch.1.16, 312.144.4-24.ch.1.17, 312.144.4-24.ch.1.18, 312.144.4-24.ch.1.19, 312.144.4-24.ch.1.20, 312.144.4-24.ch.1.21, 312.144.4-24.ch.1.22, 312.144.4-24.ch.1.23, 312.144.4-24.ch.1.24, 312.144.4-24.ch.1.25, 312.144.4-24.ch.1.26, 312.144.4-24.ch.1.27, 312.144.4-24.ch.1.28, 312.144.4-24.ch.1.29, 312.144.4-24.ch.1.30, 312.144.4-24.ch.1.31, 312.144.4-24.ch.1.32, 312.144.4-24.ch.1.33, 312.144.4-24.ch.1.34, 312.144.4-24.ch.1.35, 312.144.4-24.ch.1.36, 312.144.4-24.ch.1.37, 312.144.4-24.ch.1.38, 312.144.4-24.ch.1.39, 312.144.4-24.ch.1.40, 312.144.4-24.ch.1.41, 312.144.4-24.ch.1.42, 312.144.4-24.ch.1.43, 312.144.4-24.ch.1.44, 312.144.4-24.ch.1.45, 312.144.4-24.ch.1.46, 312.144.4-24.ch.1.47, 312.144.4-24.ch.1.48
Cyclic 24-isogeny field degree: $4$
Cyclic 24-torsion field degree: $32$
Full 24-torsion field degree: $1024$

Jacobian

Conductor: $2^{10}\cdot3^{8}$
Simple: no
Squarefree: no
Decomposition: $1^{4}$
Newforms: 36.2.a.a$^{3}$, 144.2.a.a

Models

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

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

$ 0 $ $=$ $ x^{5} - x z^{4} + 2 y^{3} z^{2} $
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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.

Canonical model
$(0:0:1:0)$, $(0:1/2:-1:1)$, $(0:0:0:1)$, $(0:-1/2:-1:1)$

Maps between models of this curve

Birational map from canonical model to plane model:

$\displaystyle X$ $=$ $\displaystyle y$
$\displaystyle Y$ $=$ $\displaystyle \frac{1}{2}x$
$\displaystyle Z$ $=$ $\displaystyle \frac{1}{2}w$

Maps to other modular curves

$j$-invariant map of degree 72 from the canonical model of this modular curve to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle 2^8\,\frac{(z^{4}-z^{2}w^{2}+w^{4})^{3}}{w^{4}z^{4}(z-w)^{2}(z+w)^{2}}$

Modular covers

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Cover information

Click on a modular curve in the diagram to see information about it.

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

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_{\mathrm{ns}}^+(3)$ $3$ $24$ $24$ $0$ $0$ full Jacobian
8.24.0.i.1 $8$ $3$ $3$ $0$ $0$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
8.24.0.i.1 $8$ $3$ $3$ $0$ $0$ full Jacobian
12.36.2.b.1 $12$ $2$ $2$ $2$ $0$ $1^{2}$
24.36.2.cj.1 $24$ $2$ $2$ $2$ $0$ $1^{2}$
24.36.2.cw.1 $24$ $2$ $2$ $2$ $0$ $1^{2}$

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

Covering curve Level Index Degree Genus Rank Kernel decomposition
24.144.7.gz.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.7.ha.1 $24$ $2$ $2$ $7$ $2$ $1^{3}$
24.144.7.hh.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.7.hi.1 $24$ $2$ $2$ $7$ $1$ $1^{3}$
24.144.7.ih.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.7.ii.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.7.il.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.7.im.1 $24$ $2$ $2$ $7$ $0$ $1^{3}$
24.144.8.fe.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fe.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.ff.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.ff.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fg.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fg.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fh.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fh.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fi.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fi.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fj.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fj.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fk.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fk.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fl.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fl.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fm.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fm.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fn.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fn.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fo.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fo.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fp.1 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.8.fp.2 $24$ $2$ $2$ $8$ $0$ $2^{2}$
24.144.9.cs.1 $24$ $2$ $2$ $9$ $1$ $1^{5}$
24.144.9.et.1 $24$ $2$ $2$ $9$ $1$ $1^{5}$
24.144.9.je.1 $24$ $2$ $2$ $9$ $1$ $1^{5}$
24.144.9.jf.1 $24$ $2$ $2$ $9$ $2$ $1^{5}$
24.144.9.mc.1 $24$ $2$ $2$ $9$ $1$ $1^{5}$
24.144.9.md.1 $24$ $2$ $2$ $9$ $0$ $1^{5}$
24.144.9.mo.1 $24$ $2$ $2$ $9$ $2$ $1^{5}$
24.144.9.mp.1 $24$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.8.j.1 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.j.2 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.l.1 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.l.2 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.n.1 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.n.2 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.p.1 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.8.p.2 $48$ $2$ $2$ $8$ $0$ $2^{2}$
48.144.9.a.1 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.a.2 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.b.1 $48$ $2$ $2$ $9$ $2$ $1^{5}$
48.144.9.b.2 $48$ $2$ $2$ $9$ $2$ $1^{5}$
48.144.9.c.1 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.c.2 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.d.1 $48$ $2$ $2$ $9$ $0$ $1^{5}$
48.144.9.d.2 $48$ $2$ $2$ $9$ $0$ $1^{5}$
48.144.9.e.1 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.e.2 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.f.1 $48$ $2$ $2$ $9$ $2$ $1^{5}$
48.144.9.f.2 $48$ $2$ $2$ $9$ $2$ $1^{5}$
48.144.9.g.1 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.g.2 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.h.1 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.9.h.2 $48$ $2$ $2$ $9$ $1$ $1^{5}$
48.144.10.j.1 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.j.2 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.l.1 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.l.2 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.n.1 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.n.2 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.p.1 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
48.144.10.p.2 $48$ $2$ $2$ $10$ $0$ $2\cdot4$
72.216.16.ch.1 $72$ $3$ $3$ $16$ $?$ not computed
120.144.7.bmh.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bmi.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bml.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bmm.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bmx.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bmy.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bnb.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.7.bnc.1 $120$ $2$ $2$ $7$ $?$ not computed
120.144.8.pi.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pi.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pj.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pj.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pk.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pk.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pl.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pl.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pm.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pm.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pn.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pn.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.po.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.po.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pp.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pp.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pq.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pq.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pr.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pr.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.ps.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.ps.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pt.1 $120$ $2$ $2$ $8$ $?$ not computed
120.144.8.pt.2 $120$ $2$ $2$ $8$ $?$ not computed
120.144.9.bbm.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.bbn.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.bby.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.bbz.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.ble.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.blf.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.blq.1 $120$ $2$ $2$ $9$ $?$ not computed
120.144.9.blr.1 $120$ $2$ $2$ $9$ $?$ not computed
168.144.7.bjb.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjc.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjf.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjg.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjr.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjs.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjv.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.7.bjw.1 $168$ $2$ $2$ $7$ $?$ not computed
168.144.8.pa.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pa.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pb.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pb.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pc.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pc.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pd.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pd.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pe.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pe.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pf.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pf.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pg.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pg.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.ph.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.ph.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pi.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pi.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pj.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pj.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pk.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pk.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pl.1 $168$ $2$ $2$ $8$ $?$ not computed
168.144.8.pl.2 $168$ $2$ $2$ $8$ $?$ not computed
168.144.9.bbe.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.bbf.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.bbq.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.bbr.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.bks.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.bkt.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.ble.1 $168$ $2$ $2$ $9$ $?$ not computed
168.144.9.blf.1 $168$ $2$ $2$ $9$ $?$ not computed
240.144.8.r.1 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.r.2 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.t.1 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.t.2 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.v.1 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.v.2 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.x.1 $240$ $2$ $2$ $8$ $?$ not computed
240.144.8.x.2 $240$ $2$ $2$ $8$ $?$ not computed
240.144.9.a.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.a.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.b.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.b.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.c.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.c.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.d.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.d.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.e.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.e.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.f.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.f.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.g.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.g.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.h.1 $240$ $2$ $2$ $9$ $?$ not computed
240.144.9.h.2 $240$ $2$ $2$ $9$ $?$ not computed
240.144.10.r.1 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.r.2 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.t.1 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.t.2 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.v.1 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.v.2 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.x.1 $240$ $2$ $2$ $10$ $?$ not computed
240.144.10.x.2 $240$ $2$ $2$ $10$ $?$ not computed
264.144.7.bjb.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjc.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjf.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjg.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjr.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjs.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjv.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.7.bjw.1 $264$ $2$ $2$ $7$ $?$ not computed
264.144.8.pb.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pb.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pc.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pc.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pd.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pd.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pe.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pe.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pf.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pf.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pg.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pg.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.ph.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.ph.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pi.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pi.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pj.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pj.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pk.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pk.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pl.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pl.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pm.1 $264$ $2$ $2$ $8$ $?$ not computed
264.144.8.pm.2 $264$ $2$ $2$ $8$ $?$ not computed
264.144.9.bbe.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bbf.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bbq.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bbr.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bkw.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bkx.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.bli.1 $264$ $2$ $2$ $9$ $?$ not computed
264.144.9.blj.1 $264$ $2$ $2$ $9$ $?$ not computed
312.144.7.bjb.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjc.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjf.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjg.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjr.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjs.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjv.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.7.bjw.1 $312$ $2$ $2$ $7$ $?$ not computed
312.144.8.pi.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pi.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pj.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pj.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pk.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pk.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pl.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pl.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pm.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pm.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pn.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pn.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.po.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.po.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pp.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pp.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pq.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pq.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pr.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pr.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.ps.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.ps.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pt.1 $312$ $2$ $2$ $8$ $?$ not computed
312.144.8.pt.2 $312$ $2$ $2$ $8$ $?$ not computed
312.144.9.bbe.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.bbf.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.bbq.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.bbr.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.bks.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.bkt.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.ble.1 $312$ $2$ $2$ $9$ $?$ not computed
312.144.9.blf.1 $312$ $2$ $2$ $9$ $?$ not computed