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Properties

Label 10.180.4.a.1
Level $10$
Index $180$
Genus $4$
Analytic rank $0$
Cusps $24$
$\Q$-cusps $4$

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Invariants

Level: $10$ $\SL_2$-level: $10$ Newform level: $50$
Index: $180$ $\PSL_2$-index:$180$
Genus: $4 = 1 + \frac{ 180 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$
Cusps: $24$ (of which $4$ are rational) Cusp widths $5^{12}\cdot10^{12}$ Cusp orbits $1^{4}\cdot2^{2}\cdot4^{4}$
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: 10B4
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 10.180.4.1

Level structure

$\GL_2(\Z/10\Z)$-generators: $\begin{bmatrix}1&5\\0&1\end{bmatrix}$, $\begin{bmatrix}3&4\\0&1\end{bmatrix}$, $\begin{bmatrix}9&0\\0&9\end{bmatrix}$
$\GL_2(\Z/10\Z)$-subgroup: $C_2^2\times C_4$
Contains $-I$: yes
Quadratic refinements: 10.360.4-10.a.1.1, 10.360.4-10.a.1.2, 10.360.4-10.a.1.3, 10.360.4-10.a.1.4, 20.360.4-10.a.1.1, 20.360.4-10.a.1.2, 20.360.4-10.a.1.3, 20.360.4-10.a.1.4, 20.360.4-10.a.1.5, 20.360.4-10.a.1.6, 20.360.4-10.a.1.7, 20.360.4-10.a.1.8, 20.360.4-10.a.1.9, 20.360.4-10.a.1.10, 20.360.4-10.a.1.11, 20.360.4-10.a.1.12, 30.360.4-10.a.1.1, 30.360.4-10.a.1.2, 30.360.4-10.a.1.3, 30.360.4-10.a.1.4, 40.360.4-10.a.1.1, 40.360.4-10.a.1.2, 40.360.4-10.a.1.3, 40.360.4-10.a.1.4, 40.360.4-10.a.1.5, 40.360.4-10.a.1.6, 40.360.4-10.a.1.7, 40.360.4-10.a.1.8, 40.360.4-10.a.1.9, 40.360.4-10.a.1.10, 40.360.4-10.a.1.11, 40.360.4-10.a.1.12, 40.360.4-10.a.1.13, 40.360.4-10.a.1.14, 40.360.4-10.a.1.15, 40.360.4-10.a.1.16, 60.360.4-10.a.1.1, 60.360.4-10.a.1.2, 60.360.4-10.a.1.3, 60.360.4-10.a.1.4, 60.360.4-10.a.1.5, 60.360.4-10.a.1.6, 60.360.4-10.a.1.7, 60.360.4-10.a.1.8, 60.360.4-10.a.1.9, 60.360.4-10.a.1.10, 60.360.4-10.a.1.11, 60.360.4-10.a.1.12, 70.360.4-10.a.1.1, 70.360.4-10.a.1.2, 70.360.4-10.a.1.3, 70.360.4-10.a.1.4, 110.360.4-10.a.1.1, 110.360.4-10.a.1.2, 110.360.4-10.a.1.3, 110.360.4-10.a.1.4, 120.360.4-10.a.1.1, 120.360.4-10.a.1.2, 120.360.4-10.a.1.3, 120.360.4-10.a.1.4, 120.360.4-10.a.1.5, 120.360.4-10.a.1.6, 120.360.4-10.a.1.7, 120.360.4-10.a.1.8, 120.360.4-10.a.1.9, 120.360.4-10.a.1.10, 120.360.4-10.a.1.11, 120.360.4-10.a.1.12, 120.360.4-10.a.1.13, 120.360.4-10.a.1.14, 120.360.4-10.a.1.15, 120.360.4-10.a.1.16, 130.360.4-10.a.1.1, 130.360.4-10.a.1.2, 130.360.4-10.a.1.3, 130.360.4-10.a.1.4, 140.360.4-10.a.1.1, 140.360.4-10.a.1.2, 140.360.4-10.a.1.3, 140.360.4-10.a.1.4, 140.360.4-10.a.1.5, 140.360.4-10.a.1.6, 140.360.4-10.a.1.7, 140.360.4-10.a.1.8, 140.360.4-10.a.1.9, 140.360.4-10.a.1.10, 140.360.4-10.a.1.11, 140.360.4-10.a.1.12, 170.360.4-10.a.1.1, 170.360.4-10.a.1.2, 170.360.4-10.a.1.3, 170.360.4-10.a.1.4, 190.360.4-10.a.1.1, 190.360.4-10.a.1.2, 190.360.4-10.a.1.3, 190.360.4-10.a.1.4, 210.360.4-10.a.1.1, 210.360.4-10.a.1.2, 210.360.4-10.a.1.3, 210.360.4-10.a.1.4, 220.360.4-10.a.1.1, 220.360.4-10.a.1.2, 220.360.4-10.a.1.3, 220.360.4-10.a.1.4, 220.360.4-10.a.1.5, 220.360.4-10.a.1.6, 220.360.4-10.a.1.7, 220.360.4-10.a.1.8, 220.360.4-10.a.1.9, 220.360.4-10.a.1.10, 220.360.4-10.a.1.11, 220.360.4-10.a.1.12, 230.360.4-10.a.1.1, 230.360.4-10.a.1.2, 230.360.4-10.a.1.3, 230.360.4-10.a.1.4, 260.360.4-10.a.1.1, 260.360.4-10.a.1.2, 260.360.4-10.a.1.3, 260.360.4-10.a.1.4, 260.360.4-10.a.1.5, 260.360.4-10.a.1.6, 260.360.4-10.a.1.7, 260.360.4-10.a.1.8, 260.360.4-10.a.1.9, 260.360.4-10.a.1.10, 260.360.4-10.a.1.11, 260.360.4-10.a.1.12, 280.360.4-10.a.1.1, 280.360.4-10.a.1.2, 280.360.4-10.a.1.3, 280.360.4-10.a.1.4, 280.360.4-10.a.1.5, 280.360.4-10.a.1.6, 280.360.4-10.a.1.7, 280.360.4-10.a.1.8, 280.360.4-10.a.1.9, 280.360.4-10.a.1.10, 280.360.4-10.a.1.11, 280.360.4-10.a.1.12, 280.360.4-10.a.1.13, 280.360.4-10.a.1.14, 280.360.4-10.a.1.15, 280.360.4-10.a.1.16, 290.360.4-10.a.1.1, 290.360.4-10.a.1.2, 290.360.4-10.a.1.3, 290.360.4-10.a.1.4, 310.360.4-10.a.1.1, 310.360.4-10.a.1.2, 310.360.4-10.a.1.3, 310.360.4-10.a.1.4, 330.360.4-10.a.1.1, 330.360.4-10.a.1.2, 330.360.4-10.a.1.3, 330.360.4-10.a.1.4
Cyclic 10-isogeny field degree: $1$
Cyclic 10-torsion field degree: $2$
Full 10-torsion field degree: $16$

Jacobian

Conductor: $2^{4}\cdot5^{8}$
Simple: no
Squarefree: yes
Decomposition: $1^{2}\cdot2$
Newforms: 50.2.a.a, 50.2.a.b, 50.2.b.a

Models

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

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

$ 0 $ $=$ $ 176 x^{6} - 220 x^{5} y + 268 x^{5} z + 32 x^{4} y^{2} - 420 x^{4} y z + 120 x^{4} z^{2} + 33 x^{3} y^{3} + \cdots + 2 z^{6} $
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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
$(1/2:1/2:1:0)$, $(1/2:0:-1/2:1)$, $(-1/2:-1:0:1)$, $(-1:1:-1:1)$

Maps between models of this curve

Birational map from canonical model to plane model:

$\displaystyle X$ $=$ $\displaystyle x-z+2w$
$\displaystyle Y$ $=$ $\displaystyle 5w$
$\displaystyle Z$ $=$ $\displaystyle 2y+z-4w$

Maps to other modular curves

$j$-invariant map of degree 180 from the canonical model of this modular curve to the modular curve $X(1)$ :

$\displaystyle j$ $=$ $\displaystyle -\frac{1}{2^5}\cdot\frac{3875877344932381023338985xyz^{28}-21977915250928928217799605xyz^{27}w-630856383790684762267567315xyz^{26}w^{2}+2152922349103887046115166565xyz^{25}w^{3}+932042765004863945004887500xyz^{24}w^{4}-106297937432947446272339252550xyz^{23}w^{5}+539733032673574185492548681550xyz^{22}w^{6}+878483306911347106416385703550xyz^{21}w^{7}-9858074901815680959889171022425xyz^{20}w^{8}+34046872198499775926352975033625xyz^{19}w^{9}+60576667133020219348676107615575xyz^{18}w^{10}-691710782961795285530140406825025xyz^{17}w^{11}+492321506637886574621136905584750xyz^{16}w^{12}+4466039650129461125621735731429500xyz^{15}w^{13}-16402127150722256120621880046859500xyz^{14}w^{14}-7385304224996646616236201780420300xyz^{13}w^{15}+187270359979936254814278553053072375xyz^{12}w^{16}-14080178476967649509853133825476275xyz^{11}w^{17}-1176248971270779898587060239049172725xyz^{10}w^{18}-205484341192675221970351745698982125xyz^{9}w^{19}+4323267635197197943774818145107894000xyz^{8}w^{20}+2257051694769458894894051246070699050xyz^{7}w^{21}-9053695196969075233008132448322442050xyz^{6}w^{22}-7945512256635206257050705320775106450xyz^{5}w^{23}+9295352333729184570079563947503089625xyz^{4}w^{24}+12588898404994870322127273213368016495xyz^{3}w^{25}-1792122786004093497328163652992593135xyz^{2}w^{26}-7681085403137002796097109724323071255xyzw^{27}-2772275126875921225710462610320803370xyw^{28}+4650048936560454097601490xz^{29}+103693613127528457406663295xz^{28}w-694047766320602333164279925xz^{27}w^{2}-2171420979139278881051377265xz^{26}w^{3}+25638270490890238482473554705xz^{25}w^{4}-170183953538626570434705291150xz^{24}w^{5}-252619374954743313699962827750xz^{23}w^{6}+4008871569690736527844823741250xz^{22}w^{7}-10844510533564094783539597765100xz^{21}w^{8}-13891684175692962159251606208275xz^{20}w^{9}+281466171290491731883542687746825xz^{19}w^{10}-395471100196813825432455375271675xz^{18}w^{11}-2021768835738163337347282826499625xz^{17}w^{12}+7476894037892565653334459918535300xz^{16}w^{13}-2639865600008929713604919290464900xz^{15}w^{14}-79513678435438014291960503515148500xz^{14}w^{15}+110886665399949692523135935783252050xz^{13}w^{16}+563306748543979758483692474590987625xz^{12}w^{17}-613691516932419689753848524358353875xz^{11}w^{18}-2574898314395638809970990950530138775xz^{10}w^{19}+1380590725696274598400219214793854975xz^{9}w^{20}+7308636010121207840373776189282810450xz^{8}w^{21}-431711640142994852805679903222733750xz^{7}w^{22}-12183885105300337872915757732434622350xz^{6}w^{23}-3739873003647857934940377857748855000xz^{5}w^{24}+10505082566257835823063322606339887755xz^{4}w^{25}+6335869083696423177038420132359455615xz^{3}w^{26}-3068049503053400990314267871044685725xz^{2}w^{27}-3058969859233848559649904681446362055xzw^{28}-498313263679612908942707111756603640xw^{29}+276057135119962219364841y^{3}z^{27}+17099892857578664945869899y^{3}z^{26}w-39183323817394204496744521y^{3}z^{25}w^{2}-526142754889879454201690975y^{3}z^{24}w^{3}+3681902845627260269206683550y^{3}z^{23}w^{4}-14447270533129336210957203990y^{3}z^{22}w^{5}-88494660014852994609078353910y^{3}z^{21}w^{6}+501395437011936133028126977590y^{3}z^{20}w^{7}-654986058750356331523565088925y^{3}z^{19}w^{8}-5255073174258714069800349497975y^{3}z^{18}w^{9}+35211751329991467323927100656565y^{3}z^{17}w^{10}+6806959568669661801699742933635y^{3}z^{16}w^{11}-336303705068254637562723865576940y^{3}z^{15}w^{12}+675529768618345147010063784251100y^{3}z^{14}w^{13}+1109642623136060146330953921400700y^{3}z^{13}w^{14}-10764056253665788371273161136293820y^{3}z^{12}w^{15}-1187849319075328430559253223134305y^{3}z^{11}w^{16}+80913767026280449350080211147337645y^{3}z^{10}w^{17}+19551512415129716167103967197413425y^{3}z^{9}w^{18}-337223134845233744100039305903826025y^{3}z^{8}w^{19}-192577717349816775688399631817562770y^{3}z^{7}w^{20}+777885061043246761920273936302473370y^{3}z^{6}w^{21}+720785569069542956202280171888862170y^{3}z^{5}w^{22}-863153634480018930379310592600645850y^{3}z^{4}w^{23}-1219649168539179773804019165473816075y^{3}z^{3}w^{24}+175578631198102341370246089831337887y^{3}z^{2}w^{25}+789481901566597393646313994233074243y^{3}zw^{26}+293378669620758818510604973004945253y^{3}w^{27}-2686004722337068044632064y^{2}z^{28}+9413814624597221534072832y^{2}z^{27}w+418205830603180572631419156y^{2}z^{26}w^{2}-1263877125557207041677853398y^{2}z^{25}w^{3}-1190020479240721080914369250y^{2}z^{24}w^{4}+72118256076380019936351095160y^{2}z^{23}w^{5}-323005037699635994132815587480y^{2}z^{22}w^{6}-644285847218580070616451901740y^{2}z^{21}w^{7}+6329635323475850447026251826020y^{2}z^{20}w^{8}-20746565865838273837295895681000y^{2}z^{19}w^{9}-45490868687333808998949713322660y^{2}z^{18}w^{10}+427930795260701890332455721228630y^{2}z^{17}w^{11}-244801623160114387969444367687910y^{2}z^{16}w^{12}-2860010354680328620008175825915920y^{2}z^{15}w^{13}+10043400608441045511439072590246000y^{2}z^{14}w^{14}+6883899318829744264182411499405080y^{2}z^{13}w^{15}-114676310810585553253234306384409640y^{2}z^{12}w^{16}-11616180486954797142667040237160720y^{2}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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
$X_0(2)$ $2$ $60$ $60$ $0$ $0$ full Jacobian
5.60.0.a.1 $5$ $3$ $3$ $0$ $0$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
5.60.0.a.1 $5$ $3$ $3$ $0$ $0$ full Jacobian
10.36.0.a.1 $10$ $5$ $5$ $0$ $0$ full Jacobian
$X_{\pm1}(10)$ $10$ $5$ $5$ $0$ $0$ full Jacobian
10.90.2.a.1 $10$ $2$ $2$ $2$ $0$ $2$

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

Covering curve Level Index Degree Genus Rank Kernel decomposition
10.360.13.a.1 $10$ $2$ $2$ $13$ $0$ $1^{5}\cdot2^{2}$
10.360.13.c.1 $10$ $2$ $2$ $13$ $0$ $1^{5}\cdot2^{2}$
20.360.13.c.1 $20$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
20.360.13.g.1 $20$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
20.360.13.i.1 $20$ $2$ $2$ $13$ $0$ $1^{5}\cdot2^{2}$
20.360.13.o.1 $20$ $2$ $2$ $13$ $0$ $1^{5}\cdot2^{2}$
20.360.13.p.1 $20$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
20.360.13.s.1 $20$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
20.360.19.cq.1 $20$ $2$ $2$ $19$ $3$ $1^{7}\cdot2^{4}$
20.360.19.cr.1 $20$ $2$ $2$ $19$ $1$ $1^{7}\cdot2^{4}$
20.360.19.dc.1 $20$ $2$ $2$ $19$ $1$ $1^{7}\cdot2^{4}$
20.360.19.de.1 $20$ $2$ $2$ $19$ $2$ $1^{7}\cdot2^{4}$
30.360.13.c.1 $30$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
30.360.13.g.1 $30$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
30.540.34.b.1 $30$ $3$ $3$ $34$ $3$ $1^{10}\cdot2^{10}$
30.720.37.a.1 $30$ $4$ $4$ $37$ $0$ $1^{17}\cdot2^{8}$
40.360.13.e.1 $40$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
40.360.13.n.1 $40$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
40.360.13.z.1 $40$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
40.360.13.bf.1 $40$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
40.360.13.bw.1 $40$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
40.360.13.bz.1 $40$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
40.360.13.ci.1 $40$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
40.360.13.cl.1 $40$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
40.360.19.sa.1 $40$ $2$ $2$ $19$ $4$ $1^{7}\cdot2^{4}$
40.360.19.sd.1 $40$ $2$ $2$ $19$ $3$ $1^{7}\cdot2^{4}$
40.360.19.tk.1 $40$ $2$ $2$ $19$ $3$ $1^{7}\cdot2^{4}$
40.360.19.tq.1 $40$ $2$ $2$ $19$ $4$ $1^{7}\cdot2^{4}$
50.900.48.a.1 $50$ $5$ $5$ $48$ $0$ $4^{3}\cdot8^{4}$
50.900.48.b.1 $50$ $5$ $5$ $48$ $0$ $4^{3}\cdot8^{4}$
50.900.48.c.1 $50$ $5$ $5$ $48$ $0$ $4^{3}\cdot8^{4}$
50.900.48.d.1 $50$ $5$ $5$ $48$ $0$ $4^{3}\cdot8^{4}$
50.900.48.e.1 $50$ $5$ $5$ $48$ $12$ $2^{6}\cdot4^{2}\cdot8^{3}$
50.900.56.a.1 $50$ $5$ $5$ $56$ $6$ $1^{2}\cdot2^{9}\cdot4^{8}$
50.900.56.a.2 $50$ $5$ $5$ $56$ $6$ $1^{2}\cdot2^{9}\cdot4^{8}$
60.360.13.p.1 $60$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
60.360.13.r.1 $60$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
60.360.13.t.1 $60$ $2$ $2$ $13$ $1$ $1^{5}\cdot2^{2}$
60.360.13.bq.1 $60$ $2$ $2$ $13$ $2$ $1^{5}\cdot2^{2}$
60.360.13.br.1 $60$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
60.360.13.bu.1 $60$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
60.360.19.pw.1 $60$ $2$ $2$ $19$ $3$ $1^{7}\cdot2^{4}$
60.360.19.px.1 $60$ $2$ $2$ $19$ $4$ $1^{7}\cdot2^{4}$
60.360.19.rs.1 $60$ $2$ $2$ $19$ $5$ $1^{7}\cdot2^{4}$
60.360.19.ru.1 $60$ $2$ $2$ $19$ $3$ $1^{7}\cdot2^{4}$
70.360.13.i.1 $70$ $2$ $2$ $13$ $3$ $1^{5}\cdot2^{2}$
70.360.13.j.1 $70$ $2$ $2$ $13$ $4$ $1^{5}\cdot2^{2}$
70.1440.97.a.1 $70$ $8$ $8$ $97$ $6$ $1^{23}\cdot2^{23}\cdot4^{6}$
70.3780.280.a.1 $70$ $21$ $21$ $280$ $50$ $1^{24}\cdot2^{48}\cdot3^{4}\cdot4^{27}\cdot6^{2}\cdot8^{3}$
70.5040.373.a.1 $70$ $28$ $28$ $373$ $56$ $1^{47}\cdot2^{71}\cdot3^{4}\cdot4^{33}\cdot6^{2}\cdot8^{3}$
110.360.13.c.1 $110$ $2$ $2$ $13$ $?$ not computed
110.360.13.d.1 $110$ $2$ $2$ $13$ $?$ not computed
120.360.13.bx.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.cd.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.cj.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.cp.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.fo.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.fr.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.ga.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.13.gd.1 $120$ $2$ $2$ $13$ $?$ not computed
120.360.19.edg.1 $120$ $2$ $2$ $19$ $?$ not computed
120.360.19.edj.1 $120$ $2$ $2$ $19$ $?$ not computed
120.360.19.ejg.1 $120$ $2$ $2$ $19$ $?$ not computed
120.360.19.ejm.1 $120$ $2$ $2$ $19$ $?$ not computed
130.360.13.i.1 $130$ $2$ $2$ $13$ $?$ not computed
130.360.13.j.1 $130$ $2$ $2$ $13$ $?$ not computed
140.360.13.v.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.13.y.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.13.z.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.13.bc.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.13.bd.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.13.bg.1 $140$ $2$ $2$ $13$ $?$ not computed
140.360.19.hs.1 $140$ $2$ $2$ $19$ $?$ not computed
140.360.19.ht.1 $140$ $2$ $2$ $19$ $?$ not computed
140.360.19.jo.1 $140$ $2$ $2$ $19$ $?$ not computed
140.360.19.jp.1 $140$ $2$ $2$ $19$ $?$ not computed
170.360.13.c.1 $170$ $2$ $2$ $13$ $?$ not computed
170.360.13.d.1 $170$ $2$ $2$ $13$ $?$ not computed
190.360.13.i.1 $190$ $2$ $2$ $13$ $?$ not computed
190.360.13.j.1 $190$ $2$ $2$ $13$ $?$ not computed
210.360.13.l.1 $210$ $2$ $2$ $13$ $?$ not computed
210.360.13.o.1 $210$ $2$ $2$ $13$ $?$ not computed
220.360.13.o.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.13.r.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.13.s.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.13.v.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.13.w.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.13.z.1 $220$ $2$ $2$ $13$ $?$ not computed
220.360.19.hs.1 $220$ $2$ $2$ $19$ $?$ not computed
220.360.19.ht.1 $220$ $2$ $2$ $19$ $?$ not computed
220.360.19.jo.1 $220$ $2$ $2$ $19$ $?$ not computed
220.360.19.jp.1 $220$ $2$ $2$ $19$ $?$ not computed
230.360.13.c.1 $230$ $2$ $2$ $13$ $?$ not computed
230.360.13.d.1 $230$ $2$ $2$ $13$ $?$ not computed
260.360.13.v.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.13.y.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.13.z.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.13.bc.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.13.bd.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.13.bg.1 $260$ $2$ $2$ $13$ $?$ not computed
260.360.19.hs.1 $260$ $2$ $2$ $19$ $?$ not computed
260.360.19.ht.1 $260$ $2$ $2$ $19$ $?$ not computed
260.360.19.jo.1 $260$ $2$ $2$ $19$ $?$ not computed
260.360.19.jp.1 $260$ $2$ $2$ $19$ $?$ not computed
280.360.13.ci.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.cl.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.cu.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.cx.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.dg.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.dj.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.ds.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.13.dv.1 $280$ $2$ $2$ $13$ $?$ not computed
280.360.19.cfw.1 $280$ $2$ $2$ $19$ $?$ not computed
280.360.19.cfz.1 $280$ $2$ $2$ $19$ $?$ not computed
280.360.19.cqi.1 $280$ $2$ $2$ $19$ $?$ not computed
280.360.19.cql.1 $280$ $2$ $2$ $19$ $?$ not computed
290.360.13.c.1 $290$ $2$ $2$ $13$ $?$ not computed
290.360.13.d.1 $290$ $2$ $2$ $13$ $?$ not computed
310.360.13.i.1 $310$ $2$ $2$ $13$ $?$ not computed
310.360.13.j.1 $310$ $2$ $2$ $13$ $?$ not computed
330.360.13.g.1 $330$ $2$ $2$ $13$ $?$ not computed
330.360.13.j.1 $330$ $2$ $2$ $13$ $?$ not computed