Invariants
| Level: | $12$ | $\SL_2$-level: | $12$ | Newform level: | $24$ | ||
| Index: | $36$ | $\PSL_2$-index: | $36$ | ||||
| Genus: | $1 = 1 + \frac{ 36 }{12} - \frac{ 6 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
| Cusps: | $3$ (all of which are rational) | Cusp widths | $12^{3}$ | Cusp orbits | $1^{3}$ | ||
| Elliptic points: | $6$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $3$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-4$) |
Other labels
| Cummins and Pauli (CP) label: | 12M1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 12.36.1.56 |
Level structure
| $\GL_2(\Z/12\Z)$-generators: | $\begin{bmatrix}7&2\\10&1\end{bmatrix}$, $\begin{bmatrix}9&1\\4&3\end{bmatrix}$, $\begin{bmatrix}9&4\\4&9\end{bmatrix}$, $\begin{bmatrix}11&3\\6&5\end{bmatrix}$ |
| $\GL_2(\Z/12\Z)$-subgroup: | $D_4\times \SD_{16}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 12-isogeny field degree: | $8$ |
| Cyclic 12-torsion field degree: | $32$ |
| Full 12-torsion field degree: | $128$ |
Jacobian
| Conductor: | $2^{3}\cdot3$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 24.2.a.a |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - x^{2} + x $ |
Rational points
This modular curve has 3 rational cusps and 1 rational CM point, but no other known rational points. The following are the known rational points on this modular curve (one row per $j$-invariant).
| Elliptic curve | CM | $j$-invariant | $j$-height | Weierstrass model | |
|---|---|---|---|---|---|
| no | $\infty$ | $0.000$ | $(0:0:1)$, $(1:-1:1)$, $(0:1:0)$ | ||
| 32.a3 | $-4$ | $1728$ | $= 2^{6} \cdot 3^{3}$ | $7.455$ | $(1:1:1)$ |
Maps to other modular curves
$j$-invariant map of degree 36 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{56x^{2}y^{14}-672x^{2}y^{13}z+2656x^{2}y^{12}z^{2}-3712x^{2}y^{11}z^{3}-1752x^{2}y^{10}z^{4}+6496x^{2}y^{9}z^{5}-95120x^{2}y^{8}z^{6}+308736x^{2}y^{7}z^{7}-93048x^{2}y^{6}z^{8}-380896x^{2}y^{5}z^{9}+115968x^{2}y^{4}z^{10}+155776x^{2}y^{3}z^{11}-20200x^{2}y^{2}z^{12}-24288x^{2}yz^{13}+3376x^{2}z^{14}+12xy^{15}-112xy^{14}z+876xy^{13}z^{2}-1456xy^{12}z^{3}-2884xy^{11}z^{4}+21552xy^{10}z^{5}+5084xy^{9}z^{6}-154448xy^{8}z^{7}-6876xy^{7}z^{8}+393072xy^{6}z^{9}+21956xy^{5}z^{10}-331728xy^{4}z^{11}-9964xy^{3}z^{12}+76496xy^{2}z^{13}-12xyz^{14}-3376xz^{15}+y^{16}+100y^{15}z-896y^{14}z^{2}+2356y^{13}z^{3}-5108y^{12}z^{4}+8596y^{11}z^{5}-16864y^{10}z^{6}+131556y^{9}z^{7}-219162y^{8}z^{8}-114452y^{7}z^{9}+272512y^{6}z^{10}+33244y^{5}z^{11}-76916y^{4}z^{12}+28y^{3}z^{13}+3424y^{2}z^{14}+12yz^{15}+z^{16}}{z^{4}(6x^{2}y^{10}+25x^{2}y^{8}z^{2}+24x^{2}y^{6}z^{4}-18x^{2}y^{4}z^{6}-6x^{2}y^{2}z^{8}+x^{2}z^{10}-15xy^{10}z-29xy^{8}z^{3}+18xy^{6}z^{5}+30xy^{4}z^{7}-3xy^{2}z^{9}-xz^{11}-y^{12}+5y^{10}z^{2}-18y^{8}z^{4}-22y^{6}z^{6}+3y^{4}z^{8}+y^{2}z^{10})}$ |
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.18.0.l.1 | $12$ | $2$ | $2$ | $0$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| 12.72.2.c.1 | $12$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 12.72.2.h.1 | $12$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 12.72.2.m.1 | $12$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 12.72.2.r.1 | $12$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 12.72.3.dn.1 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 12.72.3.dq.1 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 12.72.3.dt.1 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 12.72.3.dy.1 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 12.72.4.f.1 | $12$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 12.72.4.r.1 | $12$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 12.72.4.x.1 | $12$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 12.72.4.bc.1 | $12$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 24.72.2.x.1 | $24$ | $2$ | $2$ | $2$ | $1$ | $1$ |
| 24.72.2.bp.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.df.1 | $24$ | $2$ | $2$ | $2$ | $1$ | $1$ |
| 24.72.2.eb.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.fg.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.fi.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.gc.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.gi.1 | $24$ | $2$ | $2$ | $2$ | $1$ | $1$ |
| 24.72.2.ii.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.ik.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.io.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.2.iu.1 | $24$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 24.72.3.xr.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.yj.1 | $24$ | $2$ | $2$ | $3$ | $2$ | $1^{2}$ |
| 24.72.3.zv.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.baj.1 | $24$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 24.72.3.bcq.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.bcs.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.bes.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.bey.1 | $24$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 24.72.3.bge.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.bgg.1 | $24$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 24.72.3.bhq.1 | $24$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 24.72.3.bhw.1 | $24$ | $2$ | $2$ | $3$ | $2$ | $1^{2}$ |
| 24.72.4.cy.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.ee.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.jy.1 | $24$ | $2$ | $2$ | $4$ | $2$ | $1^{3}$ |
| 24.72.4.ky.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.lq.1 | $24$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 24.72.4.lw.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.ng.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.ni.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.nu.1 | $24$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 24.72.4.oa.1 | $24$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 24.72.4.qa.1 | $24$ | $2$ | $2$ | $4$ | $2$ | $1^{3}$ |
| 24.72.4.qc.1 | $24$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 24.72.5.fg.1 | $24$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 24.72.5.fm.1 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.72.5.fq.1 | $24$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 24.72.5.fs.1 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.72.5.ku.1 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.72.5.la.1 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 24.72.5.lu.1 | $24$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 24.72.5.lw.1 | $24$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 36.108.6.bc.1 | $36$ | $3$ | $3$ | $6$ | $2$ | $1^{5}$ |
| 36.324.20.e.1 | $36$ | $9$ | $9$ | $20$ | $9$ | $1^{9}\cdot2^{5}$ |
| 60.72.2.e.1 | $60$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 60.72.2.n.1 | $60$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 60.72.2.u.1 | $60$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 60.72.2.bd.1 | $60$ | $2$ | $2$ | $2$ | $0$ | $1$ |
| 60.72.3.bat.1 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 60.72.3.bba.1 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 60.72.3.bbj.1 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 60.72.3.bbq.1 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 60.72.4.ck.1 | $60$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 60.72.4.cs.1 | $60$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 60.72.4.da.1 | $60$ | $2$ | $2$ | $4$ | $1$ | $1^{3}$ |
| 60.72.4.di.1 | $60$ | $2$ | $2$ | $4$ | $0$ | $1^{3}$ |
| 60.180.13.nw.1 | $60$ | $5$ | $5$ | $13$ | $6$ | $1^{12}$ |
| 60.216.13.rt.1 | $60$ | $6$ | $6$ | $13$ | $1$ | $1^{12}$ |
| 60.360.25.chk.1 | $60$ | $10$ | $10$ | $25$ | $11$ | $1^{24}$ |
| 84.72.2.e.1 | $84$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 84.72.2.n.1 | $84$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 84.72.2.u.1 | $84$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 84.72.2.bd.1 | $84$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 84.72.3.ux.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 84.72.3.ve.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 84.72.3.vn.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 84.72.3.vu.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 84.72.4.cd.1 | $84$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 84.72.4.cl.1 | $84$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 84.72.4.ct.1 | $84$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 84.72.4.db.1 | $84$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 84.288.22.da.1 | $84$ | $8$ | $8$ | $22$ | $?$ | not computed |
| 120.72.2.bp.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.cx.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.fx.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.hf.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.pc.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.pe.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.py.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.qe.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.ui.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.uk.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.uo.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.2.uu.1 | $120$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 120.72.3.gfv.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.ggz.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.gkd.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.glh.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.gws.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.gwu.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.haa.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.hag.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.hby.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.hca.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.heq.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.3.hew.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.72.4.bad.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bbz.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bel.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bgh.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bna.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bng.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bpw.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bpy.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.brq.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.brw.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bvc.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.4.bve.1 | $120$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 120.72.5.bqi.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bqo.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bqs.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bqu.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.buy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bve.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bvy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.72.5.bwa.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 132.72.2.e.1 | $132$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 132.72.2.n.1 | $132$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 132.72.2.u.1 | $132$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 132.72.2.bd.1 | $132$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 132.72.3.ux.1 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 132.72.3.ve.1 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 132.72.3.vn.1 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 132.72.3.vu.1 | $132$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 132.72.4.ci.1 | $132$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 132.72.4.cq.1 | $132$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 132.72.4.cy.1 | $132$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 132.72.4.dg.1 | $132$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 156.72.2.e.1 | $156$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 156.72.2.n.1 | $156$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 156.72.2.u.1 | $156$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 156.72.2.bd.1 | $156$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 156.72.3.ux.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 156.72.3.ve.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 156.72.3.vn.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 156.72.3.vu.1 | $156$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 156.72.4.cl.1 | $156$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 156.72.4.ct.1 | $156$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 156.72.4.db.1 | $156$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 156.72.4.dj.1 | $156$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.2.bp.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.cx.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.fx.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.hf.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.pc.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.pe.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.py.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.qe.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.ui.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.uk.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.uo.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.2.uu.1 | $168$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 168.72.3.fmz.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.fod.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.frh.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.fsl.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.fzo.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.fzq.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.gcw.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.gdc.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.geu.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.gew.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.ghm.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.3.ghs.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.72.4.zf.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bbb.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bdn.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bfj.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bmc.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bmi.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.boy.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bpa.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bqs.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bqy.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bue.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.4.bug.1 | $168$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 168.72.5.bbc.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bbi.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bbm.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bbo.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bfs.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bfy.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bgs.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.72.5.bgu.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 204.72.2.e.1 | $204$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 204.72.2.n.1 | $204$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 204.72.2.u.1 | $204$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 204.72.2.bd.1 | $204$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 204.72.3.ux.1 | $204$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 204.72.3.ve.1 | $204$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 204.72.3.vn.1 | $204$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 204.72.3.vu.1 | $204$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 204.72.4.ck.1 | $204$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 204.72.4.cs.1 | $204$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 204.72.4.da.1 | $204$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 204.72.4.di.1 | $204$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 228.72.2.e.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.72.2.n.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.72.2.u.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.72.2.bd.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.72.3.ux.1 | $228$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 228.72.3.ve.1 | $228$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 228.72.3.vn.1 | $228$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 228.72.3.vu.1 | $228$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 228.72.4.cd.1 | $228$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 228.72.4.cl.1 | $228$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 228.72.4.ct.1 | $228$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 228.72.4.db.1 | $228$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.2.bp.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.cx.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.fx.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.hf.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.pc.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.pe.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.py.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.qe.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.ui.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.uk.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.uo.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.2.uu.1 | $264$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 264.72.3.fmz.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.fod.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.frh.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.fsl.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.fzo.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.fzq.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.gcw.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.gdc.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.geu.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.gew.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.ghm.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.3.ghs.1 | $264$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 264.72.4.zn.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bbj.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bdv.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bfr.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bmk.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bmq.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bpg.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bpi.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bra.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.brg.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.bum.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.4.buo.1 | $264$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 264.72.5.bbc.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bbi.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bbm.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bbo.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bfs.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bfy.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bgs.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.72.5.bgu.1 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 276.72.2.e.1 | $276$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 276.72.2.n.1 | $276$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 276.72.2.u.1 | $276$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 276.72.2.bd.1 | $276$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 276.72.3.ux.1 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 276.72.3.ve.1 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 276.72.3.vn.1 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 276.72.3.vu.1 | $276$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 276.72.4.cc.1 | $276$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 276.72.4.ck.1 | $276$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 276.72.4.cs.1 | $276$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 276.72.4.da.1 | $276$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.2.bp.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.cx.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.fx.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.hf.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.pc.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.pe.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.py.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.qe.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.ui.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.uk.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.uo.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.2.uu.1 | $312$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 312.72.3.fmz.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.fod.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.frh.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.fsl.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.fzo.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.fzq.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.gcw.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.gdc.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.geu.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.gew.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.ghm.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.3.ghs.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.72.4.bad.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bbz.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bel.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bgh.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bna.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bng.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bpw.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bpy.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.brq.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.brw.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bvc.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.4.bve.1 | $312$ | $2$ | $2$ | $4$ | $?$ | not computed |
| 312.72.5.bbc.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bbi.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bbm.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bbo.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bfs.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bfy.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bgs.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.72.5.bgu.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |