Invariants
| Level: | $48$ | $\SL_2$-level: | $48$ | Newform level: | $24$ | ||
| 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 $8$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot3^{2}\cdot6^{3}\cdot16\cdot48$ | Cusp orbits | $1^{8}\cdot2^{2}$ | ||
| 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: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 48L3 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 48.192.3.636 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}1&24\\24&37\end{bmatrix}$, $\begin{bmatrix}11&23\\0&41\end{bmatrix}$, $\begin{bmatrix}19&21\\12&23\end{bmatrix}$, $\begin{bmatrix}23&47\\12&47\end{bmatrix}$, $\begin{bmatrix}41&23\\12&5\end{bmatrix}$, $\begin{bmatrix}43&42\\12&5\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 48.96.3.qa.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: | $2^{9}\cdot3^{3}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1\cdot2$ |
| Newforms: | 24.2.a.a, 24.2.d.a |
Models
Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ x^{3} y + 2 x^{2} y^{2} - 3 x^{2} y z - x^{2} z^{2} + x y^{3} - x y^{2} z + x z^{3} + y^{3} z - y^{2} z^{2} $ |
Rational points
This modular curve has 8 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
| Canonical model |
|---|
| $(1:0:1)$, $(0:1:1)$, $(1:0:0)$, $(0:1:0)$, $(-1:1:0)$, $(0:0:1)$, $(1:1:1)$, $(1:-1:1)$ |
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{x^{24}-12x^{23}z-648x^{22}z^{2}+6944x^{21}z^{3}+143130x^{20}z^{4}-1328364x^{19}z^{5}-11042644x^{18}z^{6}+88221744x^{17}z^{7}+57792375x^{16}z^{8}-1043768016x^{15}z^{9}-311308248x^{14}z^{10}+5424551436x^{13}z^{11}+5247535396x^{12}z^{12}-7311711876x^{11}z^{13}-24143413224x^{10}z^{14}-60126662880x^{9}z^{15}-128539096857x^{8}z^{16}-123716623356x^{7}z^{17}+473107431096x^{6}z^{18}+3270504359580x^{5}z^{19}+11374932148194x^{4}z^{20}+24702174533308x^{3}z^{21}+16785212x^{2}y^{22}-318981120x^{2}y^{21}z+2417273804x^{2}y^{20}z^{2}-9521743224x^{2}y^{19}z^{3}+22040405008x^{2}y^{18}z^{4}-33625804220x^{2}y^{17}z^{5}+39675789640x^{2}y^{16}z^{6}-39183136736x^{2}y^{15}z^{7}-175672677808x^{2}y^{14}z^{8}+551327680524x^{2}y^{13}z^{9}+9482517595444x^{2}y^{12}z^{10}-83135661675712x^{2}y^{11}z^{11}+272735696742768x^{2}y^{10}z^{12}-276669339367588x^{2}y^{9}z^{13}-601552102670208x^{2}y^{8}z^{14}+1679396339847184x^{2}y^{7}z^{15}-260311874553952x^{2}y^{6}z^{16}-2931429673840160x^{2}y^{5}z^{17}+2536027811663336x^{2}y^{4}z^{18}+754447555390296x^{2}y^{3}z^{19}-1084234941836768x^{2}y^{2}z^{20}-124375378556708x^{2}yz^{21}+12594564868008x^{2}z^{22}+33561700xy^{23}-704814340xy^{22}z+6057472008xy^{21}z^{2}-27859471412xy^{20}z^{3}+76755724324xy^{19}z^{4}-137737211068xy^{18}z^{5}+172870855744xy^{17}z^{6}-153504175740xy^{16}z^{7}-55979638892xy^{15}z^{8}+197475374212xy^{14}z^{9}+7821743144460xy^{13}z^{10}-59289402920572xy^{12}z^{11}+176325782260924xy^{11}z^{12}-145020957653084xy^{10}z^{13}-439930637259284xy^{9}z^{14}+1076306801666396xy^{8}z^{15}-126038334510348xy^{7}z^{16}-1983185118304908xy^{6}z^{17}+1926478042240404xy^{5}z^{18}+506145952734384xy^{4}z^{19}-1435776610315824xy^{3}z^{20}+262700886243904xy^{2}z^{21}+342634301181240xyz^{22}-52068666045352xz^{23}+16777216y^{24}-369091484y^{23}z+3372055688y^{22}z^{2}-16776435864y^{21}z^{3}+50792387904y^{20}z^{4}-100538423564y^{19}z^{5}+136016095508y^{18}z^{6}-125972036652y^{17}z^{7}+84446034644y^{16}z^{8}-187039827484y^{15}z^{9}+156943106012y^{14}z^{10}+7622106879056y^{13}z^{11}-53525623783880y^{12}z^{12}+148542356130764y^{11}z^{13}-102331281402564y^{10}z^{14}-373325366588208y^{9}z^{15}+779177768733572y^{8}z^{16}+31173380264932y^{7}z^{17}-1376880848821700y^{6}z^{18}+1110704737266932y^{5}z^{19}+171476181845104y^{4}z^{20}-394702967238256y^{3}z^{21}+52068666080344y^{2}z^{22}-8748yz^{23}+729z^{24}}{z^{2}(x^{22}-10x^{21}z+75x^{20}z^{2}-340x^{19}z^{3}+1323x^{18}z^{4}-3500x^{17}z^{5}+8727x^{16}z^{6}-12872x^{15}z^{7}+22874x^{14}z^{8}-4764x^{13}z^{9}+13419x^{12}z^{10}+43242x^{11}z^{11}-137646x^{10}z^{12}-405822x^{9}z^{13}-1645077x^{8}z^{14}-3962054x^{7}z^{15}-5523523x^{6}z^{16}+6660024x^{5}z^{17}+80399394x^{4}z^{18}+327461936x^{3}z^{19}-21x^{2}y^{20}-6069x^{2}y^{19}z+128980x^{2}y^{18}z^{2}+164189x^{2}y^{17}z^{3}-15492462x^{2}y^{16}z^{4}+123768474x^{2}y^{15}z^{5}-590673224x^{2}y^{14}z^{6}+2493163358x^{2}y^{13}z^{7}-8717335825x^{2}y^{12}z^{8}+22071552511x^{2}y^{11}z^{9}-42326871233x^{2}y^{10}z^{10}+65587492142x^{2}y^{9}z^{11}-75331360839x^{2}y^{8}z^{12}+54109048741x^{2}y^{7}z^{13}-18590104102x^{2}y^{6}z^{14}-9292301067x^{2}y^{5}z^{15}+22266449985x^{2}y^{4}z^{16}-7780842961x^{2}y^{3}z^{17}-8151836815x^{2}y^{2}z^{18}+2429990234x^{2}yz^{19}+858962185x^{2}z^{20}-20xy^{21}-5560xy^{20}z+98737xy^{19}z^{2}+299887xy^{18}z^{3}-12333699xy^{17}z^{4}+89273043xy^{16}z^{5}-418260690xy^{15}z^{6}+1751040794xy^{14}z^{7}-5892213922xy^{13}z^{8}+14449624610xy^{12}z^{9}-27099795589xy^{11}z^{10}+40070896823xy^{10}z^{11}-42322794126xy^{9}z^{12}+24613901236xy^{8}z^{13}+2848215307xy^{7}z^{14}-21545194805xy^{6}z^{15}+22702973731xy^{5}z^{16}-7545857871xy^{4}z^{17}-7507923171xy^{3}z^{18}+6532979515xy^{2}z^{19}+1000141774xyz^{20}-1261877592xz^{21}-20y^{21}z-5579y^{20}z^{2}+93650y^{19}z^{3}+359273y^{18}z^{4}-11824408y^{17}z^{5}+81019695y^{16}z^{6}-374665808y^{15}z^{7}+1567574818y^{14}z^{8}-5179415724y^{13}z^{9}+12493698163y^{12}z^{10}-23556289436y^{11}z^{11}+35695408574y^{10}z^{12}-39842953368y^{9}z^{13}+29446587495y^{8}z^{14}-11879739086y^{7}z^{15}-3638337405y^{6}z^{16}+10066675682y^{5}z^{17}-3868044742y^{4}z^{18}-2262019366y^{3}z^{19}+1261877592y^{2}z^{20})}$ |
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $48$ | $24$ | $0$ | $0$ | full Jacobian |
| 16.48.0-16.e.1.5 | $16$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.48.0-16.e.1.5 | $16$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 24.96.1-24.ir.1.25 | $24$ | $2$ | $2$ | $1$ | $0$ | $2$ |
| 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.ka.1.17 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.ka.2.17 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.ke.1.9 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.ke.2.9 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.ki.1.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.ki.3.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.km.1.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-48.km.2.1 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.7-48.ck.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.cl.1.21 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.cz.1.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.de.2.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.eb.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ee.2.25 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ej.1.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.el.2.17 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.ex.1.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ex.2.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ey.1.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ey.2.7 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ff.1.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ff.3.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fg.2.6 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fg.4.11 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fv.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fv.2.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fz.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.fz.3.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gd.1.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gd.2.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gh.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gh.2.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.gp.1.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gq.1.11 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.gx.1.21 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.gy.2.9 | $48$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 48.384.7-48.hn.1.3 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.ho.1.19 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hv.1.19 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.7-48.hw.2.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 48.384.9-48.bar.1.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bas.2.6 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.baz.1.4 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bba.1.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfh.1.5 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfi.2.10 | $48$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfp.1.6 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bfq.1.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 48.384.9-48.bhh.1.19 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhh.2.21 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhi.2.5 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhi.4.9 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhp.1.10 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhp.2.11 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhq.1.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.bhq.2.5 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.576.13-48.bx.2.1 | $48$ | $3$ | $3$ | $13$ | $0$ | $1^{4}\cdot2^{3}$ |
| 240.384.5-240.clo.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clo.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cls.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cls.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clw.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.clw.4.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cma.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.cma.3.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.7-240.sb.1.18 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sf.2.21 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sl.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.sp.2.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tf.1.18 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tj.2.41 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tp.1.9 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.tt.2.17 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.up.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.up.4.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.uq.2.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.uq.4.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vf.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vf.3.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vg.1.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.vg.3.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wt.1.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wt.3.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wx.2.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.wx.4.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xb.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xb.2.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xf.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xf.2.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.xz.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ya.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yp.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.yq.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zv.1.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.zw.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.bal.1.33 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.bam.2.1 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.9-240.fsz.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fta.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftp.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.ftq.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fuv.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fuw.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvl.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvm.1.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdd.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdd.2.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gde.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gde.4.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdt.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdt.2.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdu.2.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.gdu.4.1 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |