Invariants
| Level: | $48$ | $\SL_2$-level: | $48$ | Newform level: | $72$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot3^{2}\cdot6^{3}\cdot16\cdot48$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 48L3 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 48.192.3.5053 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}11&32\\0&23\end{bmatrix}$, $\begin{bmatrix}19&12\\0&7\end{bmatrix}$, $\begin{bmatrix}23&34\\36&5\end{bmatrix}$, $\begin{bmatrix}31&16\\0&35\end{bmatrix}$, $\begin{bmatrix}35&11\\0&17\end{bmatrix}$, $\begin{bmatrix}47&38\\0&47\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 48.96.3.qb.1 for the level structure with $-I$) |
| Cyclic 48-isogeny field degree: | $2$ |
| Cyclic 48-torsion field degree: | $16$ |
| Full 48-torsion field degree: | $6144$ |
Jacobian
| Conductor: | $2^{9}\cdot3^{5}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1\cdot2$ |
| Newforms: | 24.2.a.a, 72.2.d.b |
Models
Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ x^{3} y - 2 x^{3} z + 3 x^{2} y^{2} - 3 x^{2} y z + 2 x y^{3} - 3 x y z^{2} + 2 x z^{3} + 3 y^{4} + \cdots + y z^{3} $ |
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 |
|---|
| $(0:0:1)$, $(1:0:1)$, $(1:0:0)$, $(-1:0:1)$ |
Maps to other modular curves
$j$-invariant map of degree 96 from the canonical model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{1}{3}\cdot\frac{16777216x^{24}+402653184x^{23}z+4026531840x^{22}z^{2}+24293408768x^{21}z^{3}+87677730816x^{20}z^{4}+261321916416x^{19}z^{5}-163208757248x^{18}z^{6}+6241527005184x^{17}z^{7}-78891989336064x^{16}z^{8}+1030447211479040x^{15}z^{9}-13716420978278400x^{14}z^{10}+184615334081200128x^{13}z^{11}-2509599336757723136x^{12}z^{12}+34406451463908753408x^{11}z^{13}-475209790221962969088x^{10}z^{14}+6606054847589107367936x^{9}z^{15}-92359280090004414529536x^{8}z^{16}+1297851167892272484188160x^{7}z^{17}-18320726481428179910131712x^{6}z^{18}+259678500111932514304524288x^{5}z^{19}-3694323992099234974839865344x^{4}z^{20}+52734265889929582412728107008x^{3}z^{21}-38403246275768492x^{2}y^{22}-326365828616093600x^{2}y^{21}z-2868550813009024944x^{2}y^{20}z^{2}-18728982546547359776x^{2}y^{19}z^{3}-111666970500366138896x^{2}y^{18}z^{4}-596410674233187604032x^{2}y^{17}z^{5}-2953783217315546822976x^{2}y^{16}z^{6}-13672542088129067649024x^{2}y^{15}z^{7}-59760479283688220246784x^{2}y^{14}z^{8}-248130906953386065997312x^{2}y^{13}z^{9}-983250064547933297251840x^{2}y^{12}z^{10}-3729861605700386930104320x^{2}y^{11}z^{11}-13568813474167476549293056x^{2}y^{10}z^{12}-47359340011016279504662528x^{2}y^{9}z^{13}-158413669815084286037372928x^{2}y^{8}z^{14}-506124887842901541268488192x^{2}y^{7}z^{15}-1533924087796752438714630144x^{2}y^{6}z^{16}-4350667236550042452352303104x^{2}y^{5}z^{17}-11236662225152981462533210112x^{2}y^{4}z^{18}-24722207002017874381333987328x^{2}y^{3}z^{19}-34235996648102826083716890624x^{2}y^{2}z^{20}+76023923045579538849916518400x^{2}yz^{21}+3712737555593938090205642752x^{2}z^{22}-12607792702475916xy^{23}-140557895231796472xy^{22}z-1235896162688139064xy^{21}z^{2}-8762085061365040656xy^{20}z^{3}-54025617801078463264xy^{19}z^{4}-300674515777503727264xy^{18}z^{5}-1537190062008637098816xy^{17}z^{6}-7332763259457032249856xy^{16}z^{7}-32936038739001609570048xy^{15}z^{8}-140313677794913376754944xy^{14}z^{9}-569820189385365298757888xy^{13}z^{10}-2213910329169602122706432xy^{12}z^{11}-8248537965448225980401664xy^{11}z^{12}-29503523641369047894960128xy^{10}z^{13}-101287728863300817391726592xy^{9}z^{14}-333102283656552324755030016xy^{8}z^{15}-1044503667858874223495479296xy^{7}z^{16}-3095381279768098928088907776xy^{6}z^{17}-8552255604818834138431291392xy^{5}z^{18}-21381711414660847050041589760xy^{4}z^{19}-39131165667895222528552861696xy^{3}z^{20}+35335712820026250806205480960xy^{2}z^{21}+49526298604651359422514987008xyz^{22}-52995248881856358561275183104xz^{23}-43122254466757031y^{24}-403961876022415308y^{23}z-3560956711453562012y^{22}z^{2}-24035603336903606136y^{21}z^{3}-145479360126813371184y^{20}z^{4}-790971079719977176064y^{19}z^{5}-3973285836122677730320y^{18}z^{6}-18640506155753955912192y^{17}z^{7}-82481728097233214806272y^{16}z^{8}-346476739359557103397888y^{15}z^{9}-1388340610898565849671424y^{14}z^{10}-5324255611814998664646400y^{13}z^{11}-19581435366027909849862656y^{12}z^{12}-69116626509172482960586752y^{11}z^{13}-233974405877943121101822976y^{10}z^{14}-757603195817664932002070528y^{9}z^{15}-2333047210563272177945677824y^{8}z^{16}-6759622542158397274270138368y^{7}z^{17}-18037771364869247774563893248y^{6}z^{18}-41839583761995139588787994624y^{5}z^{19}-66093415167556791378569068544y^{4}z^{20}+19740611340956365725800595456y^{3}z^{21}-15911471747965072778264248320y^{2}z^{22}-26497624440928179427404677120yz^{23}+12230590464z^{24}}{36691771392x^{8}z^{16}-1467670855680x^{7}z^{17}+39333578932224x^{6}z^{18}-880308979236864x^{5}z^{19}+17758597203099648x^{4}z^{20}-334947439670722560x^{3}z^{21}+356820661x^{2}y^{22}+189226418x^{2}y^{21}z+5019110779x^{2}y^{20}z^{2}+9720099906x^{2}y^{19}z^{3}+49286893449x^{2}y^{18}z^{4}+139867615860x^{2}y^{17}z^{5}+467860367076x^{2}y^{16}z^{6}+1391930375808x^{2}y^{15}z^{7}+4126545652272x^{2}y^{14}z^{8}+11818569953504x^{2}y^{13}z^{9}+33157967521888x^{2}y^{12}z^{10}+91127384528768x^{2}y^{11}z^{11}+246043810218048x^{2}y^{10}z^{12}+653789081494272x^{2}y^{9}z^{13}+1712483433708288x^{2}y^{8}z^{14}+4427586872328192x^{2}y^{7}z^{15}+11299851320770560x^{2}y^{6}z^{16}+28334156395425792x^{2}y^{5}z^{17}+68485805890932736x^{2}y^{4}z^{18}+150013701921800192x^{2}y^{3}z^{19}+224123384034770944x^{2}y^{2}z^{20}-486789694365892608x^{2}yz^{21}-17797967473803264x^{2}z^{22}+117145860xy^{23}+372310742xy^{22}z+1908037252xy^{21}z^{2}+7897595162xy^{20}z^{3}+26539032036xy^{19}z^{4}+96073350486xy^{18}z^{5}+302616451236xy^{17}z^{6}+958126682208xy^{16}z^{7}+2874205822704xy^{15}z^{8}+8438919328464xy^{14}z^{9}+24101955430672xy^{13}z^{10}+67387901673440xy^{12}z^{11}+184746792255616xy^{11}z^{12}+497798695362432xy^{10}z^{13}+1320569474445312xy^{9}z^{14}+3454292424903168xy^{8}z^{15}+8916637045859328xy^{7}z^{16}+22674381863829504xy^{6}z^{17}+56318541603268608xy^{5}z^{18}+133044606149537792xy^{4}z^{19}+249677909424529408xy^{3}z^{20}-210817507576004608xy^{2}z^{21}-318875086205485056xyz^{22}+335829216320815104xz^{23}+400632716y^{24}+560887484y^{23}z+6019522057y^{22}z^{2}+16137490762y^{21}z^{3}+67857110859y^{20}z^{4}+213560269962y^{19}z^{5}+696220671645y^{18}z^{6}+2126876788416y^{17}z^{7}+6338166431856y^{16}z^{8}+18342365707072y^{15}z^{9}+51844484115568y^{14}z^{10}+143490062317808y^{13}z^{11}+389825235957536y^{12}z^{12}+1041634011004032y^{11}z^{13}+2742115868097216y^{10}z^{14}+7122037104997632y^{9}z^{15}+18258286519985664y^{8}z^{16}+46058634840210432y^{7}z^{17}+112763677841192960y^{6}z^{18}+255034121467467776y^{5}z^{19}+424152685256716288y^{4}z^{20}-125451643083825152y^{3}z^{21}+96883861006319616y^{2}z^{22}+167914608160407552yz^{23}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.96.1-24.ir.1.24 | $24$ | $2$ | $2$ | $1$ | $0$ | $2$ |
| 48.48.0-48.e.1.1 | $48$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 48.96.1-24.ir.1.17 | $48$ | $2$ | $2$ | $1$ | $0$ | $2$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 48.384.5-48.kb.1.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kb.2.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kf.1.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kf.2.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kj.1.9 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kj.2.9 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kn.1.5 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kn.2.5 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.7-48.ci.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.cm.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.da.1.6 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.dd.2.19 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ed.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ee.1.17 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ej.1.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.em.2.19 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ez.1.7 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ez.2.7 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fa.1.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fa.2.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fh.1.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fh.2.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fi.3.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fi.4.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fw.1.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fw.2.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ga.1.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ga.2.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ge.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ge.2.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gi.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gi.2.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gr.1.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gs.1.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gz.1.3 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ha.2.6 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.hp.1.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hq.1.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hx.1.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hy.2.6 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.9-48.bat.1.7 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bau.2.5 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bbb.1.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bbc.1.4 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfj.1.11 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfk.2.5 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfr.1.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfs.1.6 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bhj.1.5 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhj.2.5 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhk.3.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhk.4.11 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhr.1.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhr.2.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhs.1.6 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhs.2.7 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.576.13-48.bz.1.17 | $48$ | $3$ | $3$ | $13$ | $0$ | $1^{4}\cdot2^{3}$ |
| 240.384.5-240.clp.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clp.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clt.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clt.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clx.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clx.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cmb.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cmb.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.7-240.sc.1.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sg.2.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sm.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sq.2.13 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tg.1.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tk.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tq.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tu.2.21 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ur.3.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ur.4.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.us.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.us.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vh.1.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vh.2.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vi.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vi.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wu.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wu.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wy.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wy.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xc.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xc.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xg.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xg.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yb.1.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yc.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yr.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ys.2.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zx.1.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zy.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ban.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.bao.2.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.9-240.ftb.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftc.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftr.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fts.1.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fux.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fuy.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvn.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvo.1.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdf.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdf.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdg.3.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdg.4.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdv.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdv.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdw.3.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdw.4.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |