Invariants
| Level: | $48$ | $\SL_2$-level: | $48$ | Newform level: | $48$ | ||
| 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 | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $1^{8}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24V3 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 48.192.3.516 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}1&8\\0&37\end{bmatrix}$, $\begin{bmatrix}7&18\\0&5\end{bmatrix}$, $\begin{bmatrix}7&32\\0&17\end{bmatrix}$, $\begin{bmatrix}11&28\\0&37\end{bmatrix}$, $\begin{bmatrix}13&14\\0&25\end{bmatrix}$, $\begin{bmatrix}31&26\\0&1\end{bmatrix}$, $\begin{bmatrix}43&46\\24&19\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.3.cl.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: | $2^{10}\cdot3^{3}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{3}$ |
| Newforms: | 24.2.a.a$^{2}$, 48.2.a.a |
Models
Embedded model Embedded model in $\mathbb{P}^{4}$
| $ 0 $ | $=$ | $ x^{2} z - 2 x y z + y^{2} z - z^{2} w - z w^{2} $ |
| $=$ | $ - 2 x^{2} t - x y t + x t^{2} + 2 y z^{2} + z w t$ | |
| $=$ | $2 x^{2} z - x y z - x z t - y^{2} z + y z t + z^{3} + z^{2} w$ | |
| $=$ | $x^{2} z - y^{2} z + y z t - 2 y w t - z^{2} w - z w^{2} + w t^{2}$ | |
| $=$ | $\cdots$ |
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 2 x^{5} y + 5 x^{4} y^{2} - 4 x^{4} z^{2} + 4 x^{3} y^{3} + x^{2} y^{4} - 8 x^{2} y^{2} z^{2} + \cdots + 4 y^{2} z^{4} $ |
Weierstrass model Weierstrass model
| $ y^{2} + \left(x^{4} + 1\right) y $ | $=$ | $ 3x^{4} $ |
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.
| Embedded model |
|---|
| $(0:0:-1:1:0)$, $(1/3:-2/3:0:1:0)$, $(0:0:0:0:1)$, $(1/3:1/3:0:0:1)$, $(1/4:1/2:0:-1/4:1)$, $(1:1:0:0:0)$, $(1/4:1/2:0:1/4:1)$, $(-1/3:2/3:0:1:0)$ |
Maps to other modular curves
$j$-invariant map of degree 96 from the embedded model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle 3\,\frac{14903410688xw^{12}t-99021821440xw^{10}t^{3}+153450539968xw^{8}t^{5}-90821520208xw^{6}t^{7}+8216821840xw^{4}t^{9}-7680644780xw^{2}t^{11}-1481053053xt^{13}-1632586752y^{14}+11428107264y^{13}t-39046033152y^{12}t^{2}+86980594176y^{11}t^{3}-143236812672y^{10}t^{4}+188394968448y^{9}t^{5}-209238793056y^{8}t^{6}+204214991616y^{7}t^{7}-179564635188y^{6}t^{8}+144108040572y^{5}t^{9}-106290896409y^{4}t^{10}+72441937818y^{3}t^{11}-45842276448y^{2}t^{12}+9041870848yw^{12}t-92828264960yw^{10}t^{3}+178238487680yw^{8}t^{5}-276130001840yw^{6}t^{7}-6657742288yw^{4}t^{9}-93867581764yw^{2}t^{11}+11402498190yt^{13}+1149239296z^{2}w^{12}-27506210048z^{2}w^{10}t^{2}+104776883072z^{2}w^{8}t^{4}-106699460912z^{2}w^{6}t^{6}+84352172096z^{2}w^{4}t^{8}-5981546836z^{2}w^{2}t^{10}+11398579086z^{2}t^{12}+1154482176zw^{13}-22832146944zw^{11}t^{2}+84289238784zw^{9}t^{4}-10177814784zw^{7}t^{6}+111313756464zw^{5}t^{8}+68350476840zw^{3}t^{10}+35874361935zwt^{12}+5242880w^{14}+438566912w^{12}t^{2}+18827724160w^{10}t^{4}+33073381856w^{8}t^{6}+126655995376w^{6}t^{8}+91680672988w^{4}t^{10}+58971703911w^{2}t^{12}-139968t^{14}}{t^{2}(32768xw^{10}t+317440xw^{8}t^{3}-10624640xw^{6}t^{5}+14850992xw^{4}t^{7}-31611412xw^{2}t^{9}-1367924xt^{11}-3779136y^{10}t^{2}+23934528y^{9}t^{3}-73798128y^{8}t^{4}+147946176y^{7}t^{5}-217099116y^{6}t^{6}+248632740y^{5}t^{7}-231111549y^{4}t^{8}+178813494y^{3}t^{9}-117042723y^{2}t^{10}+704512yw^{10}t+1021952yw^{8}t^{3}-34125952yw^{6}t^{5}-91958096yw^{4}t^{7}-183205532yw^{2}t^{9}+26724902yt^{11}-32768z^{2}w^{10}-464896z^{2}w^{8}t^{2}+1487360z^{2}w^{6}t^{4}+29929216z^{2}w^{4}t^{6}+11492224z^{2}w^{2}t^{8}+26724902z^{2}t^{10}-98304zw^{11}-1714176zw^{9}t^{2}+6098688zw^{7}t^{4}+75466416zw^{5}t^{6}+129214320zw^{3}t^{8}+91685745zwt^{10}-65536w^{12}-1593344w^{10}t^{2}+4222720w^{8}t^{4}+61848752w^{6}t^{6}+161928524w^{4}t^{8}+140577553w^{2}t^{10})}$ |
Map of degree 1 from the embedded model of this modular curve to the plane model of the modular curve 24.96.3.cl.1 :
| $\displaystyle X$ | $=$ | $\displaystyle z$ |
| $\displaystyle Y$ | $=$ | $\displaystyle 2w$ |
| $\displaystyle Z$ | $=$ | $\displaystyle \frac{1}{2}t$ |
Equation of the image curve:
| $0$ | $=$ | $ 2X^{5}Y+5X^{4}Y^{2}+4X^{3}Y^{3}+X^{2}Y^{4}-4X^{4}Z^{2}-8X^{2}Y^{2}Z^{2}-12XY^{3}Z^{2}-4Y^{4}Z^{2}+8XYZ^{4}+4Y^{2}Z^{4} $ |
Map of degree 1 from the embedded model of this modular curve to the Weierstrass model of the modular curve 24.96.3.cl.1 :
| $\displaystyle X$ | $=$ | $\displaystyle 2z^{6}w+\frac{1}{2}z^{6}t+6z^{5}w^{2}+3z^{5}wt+\frac{1}{2}z^{5}t^{2}+4z^{4}w^{3}+6z^{4}w^{2}t+z^{4}wt^{2}+\frac{1}{4}z^{4}t^{3}+4z^{3}w^{3}t-3z^{3}w^{2}t^{2}+\frac{1}{2}z^{3}wt^{3}+\frac{1}{2}z^{3}t^{4}-4z^{2}w^{3}t^{2}-3z^{2}w^{2}t^{3}+\frac{1}{8}z^{2}t^{5}-4zw^{3}t^{3}-zw^{2}t^{4}-\frac{3}{4}zwt^{5}-\frac{1}{8}zt^{6}-w^{2}t^{5}-\frac{1}{4}wt^{6}$ |
| $\displaystyle Y$ | $=$ | $\displaystyle \frac{1}{16}z^{24}t^{4}+\frac{5}{4}z^{23}wt^{4}+\frac{3}{8}z^{23}t^{5}+2z^{22}w^{2}t^{4}+3z^{22}wt^{5}+\frac{3}{4}z^{22}t^{6}+z^{21}w^{3}t^{4}+\frac{15}{4}z^{21}w^{2}t^{5}+\frac{17}{4}z^{21}wt^{6}+\frac{9}{8}z^{21}t^{7}+\frac{3}{2}z^{20}w^{3}t^{5}+\frac{9}{2}z^{20}w^{2}t^{6}+\frac{45}{8}z^{20}wt^{7}+\frac{45}{32}z^{20}t^{8}+\frac{3}{2}z^{19}w^{3}t^{6}+6z^{19}w^{2}t^{7}+\frac{15}{4}z^{19}wt^{8}+\frac{33}{32}z^{19}t^{9}+\frac{9}{4}z^{18}w^{3}t^{7}+\frac{15}{8}z^{18}w^{2}t^{8}+\frac{9}{16}z^{18}wt^{9}+\frac{17}{32}z^{18}t^{10}-\frac{33}{16}z^{17}w^{2}t^{9}-\frac{11}{8}z^{17}wt^{10}+\frac{3}{64}z^{17}t^{11}-\frac{3}{2}z^{16}w^{3}t^{9}-\frac{55}{16}z^{16}w^{2}t^{10}-\frac{57}{16}z^{16}wt^{11}-\frac{117}{256}z^{16}t^{12}-\frac{13}{8}z^{15}w^{3}t^{10}-\frac{201}{32}z^{15}w^{2}t^{11}-\frac{175}{64}z^{15}wt^{12}-\frac{45}{128}z^{15}t^{13}-\frac{51}{16}z^{14}w^{3}t^{11}-\frac{27}{8}z^{14}w^{2}t^{12}-\frac{45}{64}z^{14}wt^{13}-\frac{3}{16}z^{14}t^{14}-\frac{3}{2}z^{13}w^{3}t^{12}-\frac{15}{64}z^{13}w^{2}t^{13}+\frac{3}{32}z^{13}wt^{14}-\frac{21}{256}z^{13}t^{15}+\frac{27}{64}z^{12}w^{2}t^{14}+\frac{63}{64}z^{12}wt^{15}+\frac{51}{512}z^{12}t^{16}+\frac{3}{32}z^{11}w^{3}t^{14}+\frac{255}{128}z^{11}w^{2}t^{15}+\frac{3}{4}z^{11}wt^{16}+\frac{3}{64}z^{11}t^{17}+\frac{69}{64}z^{10}w^{3}t^{15}+\frac{9}{8}z^{10}w^{2}t^{16}+\frac{15}{256}z^{10}wt^{17}+\frac{39}{64}z^{9}w^{3}t^{16}-\frac{3}{128}z^{9}w^{2}t^{17}-\frac{15}{256}z^{9}wt^{18}+\frac{9}{1024}z^{9}t^{19}-\frac{3}{128}z^{8}w^{3}t^{17}-\frac{15}{256}z^{8}w^{2}t^{18}-\frac{63}{512}z^{8}wt^{19}-\frac{51}{4096}z^{8}t^{20}-\frac{129}{512}z^{7}w^{2}t^{19}-\frac{87}{1024}z^{7}wt^{20}-\frac{3}{1024}z^{7}t^{21}-\frac{9}{64}z^{6}w^{3}t^{19}-\frac{75}{512}z^{6}w^{2}t^{20}+\frac{9}{512}z^{6}wt^{21}+\frac{11}{2048}z^{6}t^{22}-\frac{3}{32}z^{5}w^{3}t^{20}+\frac{21}{512}z^{5}w^{2}t^{21}+\frac{5}{256}z^{5}wt^{22}+\frac{3}{128}z^{4}w^{3}t^{21}+\frac{13}{512}z^{4}w^{2}t^{22}-\frac{3}{4096}z^{4}t^{24}+\frac{1}{64}z^{3}w^{3}t^{22}-\frac{1}{1024}z^{3}wt^{24}$ |
| $\displaystyle Z$ | $=$ | $\displaystyle \frac{1}{2}z^{6}t+\frac{1}{2}z^{5}t^{2}+\frac{1}{4}z^{4}t^{3}+\frac{1}{4}z^{3}t^{4}-\frac{1}{8}z^{2}t^{5}-\frac{1}{8}zt^{6}$ |
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 |
| 16.48.0-8.i.1.2 | $16$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.48.0-8.i.1.2 | $16$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 48.96.1-24.ir.1.15 | $48$ | $2$ | $2$ | $1$ | $0$ | $1^{2}$ |
| 48.96.1-24.ir.1.17 | $48$ | $2$ | $2$ | $1$ | $0$ | $1^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 48.384.5-24.df.1.11 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.df.2.2 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.df.3.11 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.df.4.2 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.dg.1.14 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.dg.2.2 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.dg.3.14 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.5-24.dg.4.2 | $48$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 48.384.7-48.cg.1.38 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.1.39 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.2.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.2.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.3.26 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.3.29 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.4.5 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.cg.4.6 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ci.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ci.1.33 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ci.2.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ci.2.21 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ck.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ck.1.17 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ck.2.33 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-48.ck.2.35 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.db.1.14 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.db.2.15 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.db.3.12 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.db.4.15 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dj.1.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dj.2.2 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dk.1.8 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dk.2.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dl.1.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dl.2.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dl.3.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dl.4.1 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dm.1.9 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dm.2.11 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dn.1.13 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dn.2.15 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.do.1.4 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.do.2.8 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dp.1.18 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dp.2.20 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dr.1.14 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dr.2.15 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dr.3.12 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.7-24.dr.4.15 | $48$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 48.384.9-24.bi.2.12 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{6}$ |
| 48.384.9-24.cv.1.16 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-24.ey.1.12 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-24.ez.1.16 | $48$ | $2$ | $2$ | $9$ | $3$ | $1^{6}$ |
| 48.384.9-24.ge.1.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-24.ge.2.3 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-24.gf.1.2 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-24.gf.2.2 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hn.1.3 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.hn.1.17 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.hn.2.38 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.ho.1.7 | $48$ | $2$ | $2$ | $9$ | $3$ | $1^{6}$ |
| 48.384.9-48.ho.1.35 | $48$ | $2$ | $2$ | $9$ | $3$ | $1^{6}$ |
| 48.384.9-48.ho.2.26 | $48$ | $2$ | $2$ | $9$ | $3$ | $1^{6}$ |
| 48.384.9-48.hp.1.1 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hp.2.39 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hp.2.45 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hp.3.1 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hp.4.39 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hp.4.45 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.1.1 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.2.38 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.2.42 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.3.1 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.4.32 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hq.4.36 | $48$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 48.384.9-48.hr.1.6 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.hr.1.35 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.hr.2.13 | $48$ | $2$ | $2$ | $9$ | $1$ | $1^{6}$ |
| 48.384.9-48.hs.1.2 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{6}$ |
| 48.384.9-48.hs.1.17 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{6}$ |
| 48.384.9-48.hs.2.31 | $48$ | $2$ | $2$ | $9$ | $0$ | $1^{6}$ |
| 48.384.11-48.g.1.7 | $48$ | $2$ | $2$ | $11$ | $0$ | $2^{2}\cdot4$ |
| 48.384.11-48.g.2.1 | $48$ | $2$ | $2$ | $11$ | $0$ | $2^{2}\cdot4$ |
| 48.384.11-48.k.1.7 | $48$ | $2$ | $2$ | $11$ | $0$ | $2^{2}\cdot4$ |
| 48.384.11-48.k.2.25 | $48$ | $2$ | $2$ | $11$ | $0$ | $2^{2}\cdot4$ |
| 48.384.11-48.m.1.1 | $48$ | $2$ | $2$ | $11$ | $0$ | $4^{2}$ |
| 48.384.11-48.m.2.33 | $48$ | $2$ | $2$ | $11$ | $0$ | $4^{2}$ |
| 48.384.11-48.m.3.1 | $48$ | $2$ | $2$ | $11$ | $0$ | $4^{2}$ |
| 48.384.11-48.m.4.21 | $48$ | $2$ | $2$ | $11$ | $0$ | $4^{2}$ |
| 48.576.13-24.ec.1.2 | $48$ | $3$ | $3$ | $13$ | $0$ | $1^{10}$ |
| 240.384.5-120.qx.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qx.2.23 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qx.3.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qx.4.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qy.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qy.2.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qy.3.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-120.qy.4.20 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.7-120.jl.1.3 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jl.2.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jl.3.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jl.4.2 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jt.1.27 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jt.2.30 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.ju.1.19 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.ju.2.14 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jv.1.8 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jv.2.16 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jv.3.12 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jv.4.24 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jw.1.10 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jw.2.4 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jx.1.11 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jx.2.12 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jy.1.25 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jy.2.8 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jz.1.61 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.jz.2.48 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.1.5 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.1.17 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.2.76 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.2.94 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.3.68 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.3.82 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.4.17 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ka.4.53 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.kb.1.12 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.kb.2.8 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.kb.3.13 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-120.kb.4.8 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.kc.1.4 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.kc.1.74 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.kc.2.25 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.kc.2.45 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ke.1.8 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ke.1.18 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ke.2.65 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.7-240.ke.2.69 | $240$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 240.384.9-120.oi.1.19 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.oj.1.22 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.ou.1.20 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.ov.1.12 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.sm.1.16 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.sm.2.24 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.sn.1.8 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-120.sn.2.12 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsb.1.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsb.1.33 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsb.2.84 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsc.1.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsc.1.83 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsc.2.52 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.1.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.2.82 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.2.90 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.3.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.4.74 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsd.4.94 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.1.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.2.66 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.2.70 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.3.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.4.38 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bse.4.48 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsf.1.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsf.1.75 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsf.2.28 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsg.1.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsg.1.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.9-240.bsg.2.68 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 240.384.11-240.s.1.7 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.s.2.10 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.u.1.7 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.u.2.50 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.w.1.1 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.w.2.68 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.w.3.1 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |
| 240.384.11-240.w.4.40 | $240$ | $2$ | $2$ | $11$ | $?$ | not computed |