Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $48$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12P1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.96.1.53 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&18\\18&19\end{bmatrix}$, $\begin{bmatrix}7&20\\0&19\end{bmatrix}$, $\begin{bmatrix}11&18\\12&11\end{bmatrix}$, $\begin{bmatrix}11&18\\18&17\end{bmatrix}$, $\begin{bmatrix}23&2\\18&13\end{bmatrix}$, $\begin{bmatrix}23&6\\6&17\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | Group 768.1076118 |
| Contains $-I$: | no $\quad$ (see 12.48.1.a.1 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $4$ |
| Cyclic 24-torsion field degree: | $32$ |
| Full 24-torsion field degree: | $768$ |
Jacobian
| Conductor: | $2^{4}\cdot3$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 48.2.a.a |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + x^{2} - 4x - 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.
| Weierstrass model |
|---|
| $(2:0:1)$, $(-1:0:1)$, $(0:1:0)$, $(-2:0:1)$ |
Maps to other modular curves
$j$-invariant map of degree 48 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{16x^{2}y^{14}+254370x^{2}y^{12}z^{2}+272792952x^{2}y^{10}z^{4}+43885840685x^{2}y^{8}z^{6}+1881465528280x^{2}y^{6}z^{8}+31188954184569x^{2}y^{4}z^{10}+218165771777620x^{2}y^{2}z^{12}+541652977285693x^{2}z^{14}+852xy^{14}z+2923620xy^{12}z^{3}+2032924815xy^{10}z^{5}+217907337732xy^{8}z^{7}+7546917207824xy^{6}z^{9}+109553117422806xy^{4}z^{11}+699635304814401xy^{2}z^{13}+1624959302500352xz^{15}+y^{16}+11420y^{14}z^{2}+33883710y^{12}z^{4}+9961460717y^{10}z^{6}+628484953611y^{8}z^{8}+14424778023672y^{6}z^{10}+146070717545179y^{4}z^{12}+662020649013103y^{2}z^{14}+1083306712635148z^{16}}{zy^{4}(77x^{2}y^{8}z-128x^{2}y^{6}z^{3}-1280x^{2}y^{4}z^{5}-2048x^{2}y^{2}z^{7}+16384x^{2}z^{9}+xy^{10}+224xy^{8}z^{2}+384xy^{6}z^{4}+2048xy^{4}z^{6}+6144xy^{2}z^{8}-16384xz^{10}+15y^{10}z-20y^{8}z^{3}+1280y^{4}z^{7}-8192y^{2}z^{9}-32768z^{11})}$ |
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 |
|---|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $24$ | $12$ | $0$ | $0$ | full Jacobian |
| 8.24.0-4.a.1.2 | $8$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.24.0-4.a.1.2 | $8$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 24.48.0-12.f.1.5 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 24.48.0-12.f.1.8 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.192.1-12.a.1.5 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 24.192.1-12.a.2.7 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 24.192.1-24.ci.1.6 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 24.192.1-24.ci.2.10 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 24.192.3-12.a.1.11 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-12.b.1.28 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-12.c.1.8 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-12.d.1.10 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-24.d.1.16 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-24.e.1.16 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-12.f.1.10 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-12.f.2.15 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bb.1.14 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-24.bd.1.14 | $24$ | $2$ | $2$ | $3$ | $2$ | $1^{2}$ |
| 24.192.3-24.bi.1.8 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bi.1.9 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bi.2.8 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bi.2.9 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bj.1.5 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bj.1.6 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bj.2.5 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bj.2.6 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bs.1.20 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.bs.2.22 | $24$ | $2$ | $2$ | $3$ | $0$ | $2$ |
| 24.192.3-24.ce.1.16 | $24$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 24.192.3-24.cf.1.10 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-24.ci.1.4 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.3-24.cj.1.5 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.192.5-24.a.1.20 | $24$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 24.192.5-24.b.1.22 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.192.5-24.e.1.10 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.192.5-24.f.1.10 | $24$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 24.192.5-24.i.1.4 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.i.1.6 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.i.2.4 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.i.2.10 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.j.1.5 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.j.1.6 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.j.2.8 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.192.5-24.j.2.11 | $24$ | $2$ | $2$ | $5$ | $0$ | $4$ |
| 24.288.5-12.a.1.10 | $24$ | $3$ | $3$ | $5$ | $0$ | $1^{4}$ |
| 72.288.5-36.a.1.9 | $72$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 72.288.9-36.a.1.15 | $72$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 72.288.9-36.e.1.20 | $72$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 120.192.1-60.a.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-60.a.2.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.le.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.1-120.le.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.192.3-60.a.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-60.b.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-60.d.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-60.e.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-60.k.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-60.k.2.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.do.1.40 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.dq.1.40 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.dv.1.40 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.dx.1.40 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.eo.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.eo.1.17 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.eo.2.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.eo.2.24 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ep.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ep.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ep.2.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ep.2.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ey.1.33 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ey.2.33 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fw.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.fx.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.ga.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.3-120.gb.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.192.5-120.a.1.20 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.b.1.37 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.e.1.24 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.f.1.29 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.i.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.i.1.22 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.i.2.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.i.2.18 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.j.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.j.1.19 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.j.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.192.5-120.j.2.20 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.480.17-60.a.1.47 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
| 168.192.1-84.a.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-84.a.2.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.le.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.le.2.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.3-84.a.1.27 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-84.b.1.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-84.d.1.20 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-84.e.1.16 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-84.k.1.30 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-84.k.2.20 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.cq.1.39 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.cs.1.39 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.cx.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.cz.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dq.1.6 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dq.1.23 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dq.2.6 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dq.2.23 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dr.1.14 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dr.1.19 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dr.2.12 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.dr.2.18 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.ea.1.42 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.ea.2.38 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.ey.1.29 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.ez.1.19 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.fc.1.11 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.fd.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.5-168.a.1.32 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.b.1.28 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.e.1.24 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.f.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.i.1.18 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.i.1.43 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.i.2.10 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.i.2.39 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.j.1.22 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.j.1.41 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.j.2.22 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.192.5-168.j.2.41 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.1-132.a.1.9 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-132.a.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.le.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.1-264.le.2.20 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.192.3-132.a.1.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-132.b.1.26 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-132.d.1.28 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-132.e.1.18 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-132.k.1.32 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-132.k.2.30 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cq.1.39 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cs.1.39 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cx.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.cz.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dq.1.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dq.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dq.2.9 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dq.2.23 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dr.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dr.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dr.2.3 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.dr.2.20 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ea.1.36 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ea.2.34 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ey.1.27 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.ez.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fc.1.7 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.3-264.fd.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.192.5-264.a.1.32 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.b.1.36 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.e.1.8 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.f.1.16 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.i.1.3 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.i.1.20 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.i.2.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.i.2.34 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.j.1.7 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.j.1.19 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.j.2.9 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.192.5-264.j.2.38 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
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| 312.192.1-156.a.2.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.le.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.le.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.3-156.a.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-156.b.1.20 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-156.d.1.18 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-156.e.1.22 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-156.k.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-156.k.2.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.do.1.39 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.dq.1.39 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.dv.1.40 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.dx.1.40 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.eo.1.10 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.eo.1.18 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.eo.2.14 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.eo.2.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ep.1.2 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ep.1.22 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ep.2.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ep.2.21 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ey.1.36 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ey.2.38 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.fw.1.9 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.fx.1.11 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ga.1.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.gb.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.5-312.a.1.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.b.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.e.1.24 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.f.1.34 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.i.1.11 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.i.1.19 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.i.2.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.i.2.23 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.j.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.j.1.19 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.j.2.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.192.5-312.j.2.17 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |