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: | 48.192.3.4957 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}5&11\\36&37\end{bmatrix}$, $\begin{bmatrix}11&17\\12&7\end{bmatrix}$, $\begin{bmatrix}13&35\\24&43\end{bmatrix}$, $\begin{bmatrix}31&8\\36&41\end{bmatrix}$, $\begin{bmatrix}31&24\\12&13\end{bmatrix}$, $\begin{bmatrix}37&32\\24&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 48.96.3.qb.2 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 $ | $=$ | $ 2 x^{3} y + x^{3} z - 3 x^{2} y z - 2 x y^{3} - 3 x y^{2} z - x z^{3} + y^{3} z + 3 y^{2} z^{2} + \cdots + 3 z^{4} $ |
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 |
|---|
| $(1:1:0)$, $(1:0:0)$, $(-1:1:0)$, $(0:1:0)$ |
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}{2\cdot3}\cdot\frac{191102976x^{24}-2293235712x^{23}z+14906032128x^{22}z^{2}-67268247552x^{21}z^{3}+232691761152x^{20}z^{4}-649415688192x^{19}z^{5}+1564572008448x^{18}z^{6}-3481024315392x^{17}z^{7}+7711809057792x^{16}z^{8}-17265371553792x^{15}z^{9}+37764165897216x^{14}z^{10}-76365848798208x^{13}z^{11}+144716294774016x^{12}z^{12}-258855841663488x^{11}z^{13}+471284280370944x^{10}z^{14}-840391203732480x^{9}z^{15}+1507962104503704x^{8}z^{16}-2435731463046240x^{7}z^{17}+4067329211527536x^{6}z^{18}-5815801642394880x^{5}z^{19}+10271040321886389x^{4}z^{20}-12699707457354714x^{3}z^{21}+102738366308024320x^{2}y^{22}+1130122029388267520x^{2}y^{21}z+5627036615251722240x^{2}y^{20}z^{2}+16716095123927859200x^{2}y^{19}z^{3}+32209568379145289728x^{2}y^{18}z^{4}+38936749243322990592x^{2}y^{17}z^{5}+19349965486881914880x^{2}y^{16}z^{6}-28164764245094694912x^{2}y^{15}z^{7}-77030487129094244352x^{2}y^{14}z^{8}-90327653694323750912x^{2}y^{13}z^{9}-55794785157485309440x^{2}y^{12}z^{10}+1273949869907149824x^{2}y^{11}z^{11}+42929906922098862848x^{2}y^{10}z^{12}+51845783264873459968x^{2}y^{9}z^{13}+38131855424760219264x^{2}y^{8}z^{14}+20655832108512251904x^{2}y^{7}z^{15}+9568819446695681520x^{2}y^{6}z^{16}+4653480211164814032x^{2}y^{5}z^{17}+2561041478556099748x^{2}y^{4}z^{18}+1331407478088523928x^{2}y^{3}z^{19}+572215566868666284x^{2}y^{2}z^{20}+176874010220055896x^{2}yz^{21}+52403126257168555x^{2}z^{22}+102456891522678784xy^{23}+1075515886202781696xy^{22}z+5040794625680605184xy^{21}z^{2}+13804799541305409536xy^{20}z^{3}+23412490677413019648xy^{19}z^{4}+20968180346502086656xy^{18}z^{5}-6293944113787207680xy^{17}z^{6}-52845854691305963520xy^{16}z^{7}-89839299563064754176xy^{15}z^{8}-87748555723345688576xy^{14}z^{9}-46660357520470262784xy^{13}z^{10}+1440595018658170880xy^{12}z^{11}+23081901020600662784xy^{11}z^{12}+12084075393680806272xy^{10}z^{13}-12284706374653780352xy^{9}z^{14}-28706758654568774016xy^{8}z^{15}-30344156673708099456xy^{7}z^{16}-22753843563769546416xy^{6}z^{17}-13639671741153192056xy^{5}z^{18}-6933387140177590632xy^{4}z^{19}-3052299323009029714xy^{3}z^{20}-1144283270236163359xy^{2}z^{21}-332381964789699759xyz^{22}-71593029158354255xz^{23}+262144y^{24}-51228445758193664y^{23}z-640285203158401024y^{22}z^{2}-3648197173600059392y^{21}z^{3}-12687766036043431936y^{20}z^{4}-30086912865093779456y^{19}z^{5}-50356917151357730816y^{18}z^{6}-56855518473161637888y^{17}z^{7}-30671926069331684352y^{16}z^{8}+30552450220024225792y^{15}z^{9}+101840157984314833408y^{14}z^{10}+144364516134172845056y^{13}z^{11}+135519155143658028544y^{12}z^{12}+87059462885287879808y^{11}z^{13}+33167609349825134848y^{10}z^{14}+1438422915243747712y^{9}z^{15}-4349354539578313512y^{8}z^{16}+2373266463455900064y^{7}z^{17}+8105798634485071276y^{6}z^{18}+8428404934385007208y^{5}z^{19}+5653612835510742551y^{4}z^{20}+2805969298739117227y^{3}z^{21}+1102348734897792836y^{2}z^{22}+326626390709545549yz^{23}+73432743319458034z^{24}}{z^{2}(13436928x^{18}z^{4}-120932352x^{17}z^{5}+634894848x^{16}z^{6}-2338025472x^{15}z^{7}+6696628992x^{14}z^{8}-15554923776x^{13}z^{9}+30181439808x^{12}z^{10}-49620055680x^{11}z^{11}+69610267944x^{10}z^{12}-83307326472x^{9}z^{13}+83613974490x^{8}z^{14}-68235607224x^{7}z^{15}+38349924174x^{6}z^{16}-5113052910x^{5}z^{17}-31153248567x^{4}z^{18}+48624804468x^{3}z^{19}-32768x^{2}y^{20}-327680x^{2}y^{19}z-1261568x^{2}y^{18}z^{2}-2015232x^{2}y^{17}z^{3}-12650496x^{2}y^{16}z^{4}-97861632x^{2}y^{15}z^{5}-506671104x^{2}y^{14}z^{6}-1782312960x^{2}y^{13}z^{7}-5666047104x^{2}y^{12}z^{8}-15510653696x^{2}y^{11}z^{9}-39657778112x^{2}y^{10}z^{10}-86264308544x^{2}y^{9}z^{11}-170746434552x^{2}y^{8}z^{12}-285398267232x^{2}y^{7}z^{13}-428878924248x^{2}y^{6}z^{14}-532344531192x^{2}y^{5}z^{15}-583774038672x^{2}y^{4}z^{16}-499358597064x^{2}y^{3}z^{17}-364083060914x^{2}y^{2}z^{18}-172568024306x^{2}yz^{19}-115241156093x^{2}z^{20}+32768xy^{20}z+278528xy^{19}z^{2}+794624xy^{18}z^{3}+319488xy^{17}z^{4}+10143744xy^{16}z^{5}+260431872xy^{15}z^{6}+1728454656xy^{14}z^{7}+7427066880xy^{13}z^{8}+23880876672xy^{12}z^{9}+64404814016xy^{11}z^{10}+148776248672xy^{10}z^{11}+304011196640xy^{9}z^{12}+545878588440xy^{8}z^{13}+863705891064xy^{7}z^{14}+1187069152908xy^{6}z^{15}+1403472739020xy^{5}z^{16}+1404239974368xy^{4}z^{17}+1155097172814xy^{3}z^{18}+756821570741xy^{2}z^{19}+348146915873xyz^{20}+132019451195xz^{21}+32768y^{22}+360448y^{21}z+1589248y^{20}z^{2}+3301376y^{19}z^{3}+1425408y^{18}z^{4}-9904128y^{17}z^{5}-30269952y^{16}z^{6}-132096000y^{15}z^{7}-826204800y^{14}z^{8}-3965263744y^{13}z^{9}-14142494336y^{12}z^{10}-40319596640y^{11}z^{11}-97198592944y^{10}z^{12}-202584355632y^{9}z^{13}-374147179194y^{8}z^{14}-603279440820y^{7}z^{15}-859357003974y^{6}z^{16}-1042642912290y^{5}z^{17}-1095958528285y^{4}z^{18}-930272366729y^{3}z^{19}-661812816158y^{2}z^{20}-319328262361yz^{21}-125985953904z^{22})}$ |
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.1.11 | $24$ | $2$ | $2$ | $1$ | $0$ | $2$ |
| 48.48.0-48.e.2.1 | $48$ | $4$ | $4$ | $0$ | $0$ | 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.3.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kb.4.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kf.3.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kf.4.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kj.3.2 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kj.4.3 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kn.3.5 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.kn.4.9 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.7-48.ci.2.21 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.cm.1.21 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.da.1.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.dd.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ed.2.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ee.2.25 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ej.2.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.em.1.17 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ez.3.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ez.4.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fa.3.10 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fa.4.11 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fh.3.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fh.4.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fi.1.10 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fi.2.11 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fw.3.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fw.4.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ga.3.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ga.4.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ge.3.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ge.4.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gi.3.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gi.4.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gr.2.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gs.2.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gz.2.4 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ha.1.2 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.hp.2.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hq.2.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hx.2.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hy.1.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.9-48.bat.2.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bau.1.18 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bbb.2.18 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bbc.2.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfj.2.3 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfk.1.18 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfr.2.18 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfs.2.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bhj.3.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhj.4.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhk.1.9 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhk.2.9 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhr.3.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhr.4.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhs.3.9 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhs.4.9 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.576.13-48.bz.2.5 | $48$ | $3$ | $3$ | $13$ | $0$ | $1^{4}\cdot2^{3}$ |
| 240.384.5-240.clp.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clp.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clt.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clt.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clx.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clx.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cmb.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cmb.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.7-240.sc.2.25 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sg.1.21 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sm.2.13 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sq.1.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tg.2.25 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tk.2.41 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tq.2.21 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tu.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ur.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ur.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.us.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.us.2.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vh.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vh.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vi.3.17 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vi.4.17 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wu.3.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wu.4.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wy.1.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wy.2.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xc.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xc.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xg.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xg.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yb.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yc.2.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yr.2.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ys.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zx.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zy.2.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ban.2.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.bao.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.9-240.ftb.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftc.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftr.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fts.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fux.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fuy.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvn.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvo.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdf.3.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdf.4.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdg.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdg.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdv.3.2 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdv.4.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdw.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdw.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |