Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | 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 | $2^{2}\cdot4^{3}\cdot6^{2}\cdot8\cdot12^{3}\cdot24$ | 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: | 24AA3 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.192.3.103 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}7&16\\12&17\end{bmatrix}$, $\begin{bmatrix}11&4\\12&7\end{bmatrix}$, $\begin{bmatrix}17&10\\12&1\end{bmatrix}$, $\begin{bmatrix}17&12\\0&17\end{bmatrix}$, $\begin{bmatrix}19&18\\0&17\end{bmatrix}$, $\begin{bmatrix}23&20\\12&7\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $C_{12}:C_2^5$ |
| Contains $-I$: | no $\quad$ (see 24.96.3.bq.2 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $2$ |
| Cyclic 24-torsion field degree: | $16$ |
| Full 24-torsion field degree: | $384$ |
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 - x^{3} z - x^{2} y^{2} + x^{2} y z + 2 x^{2} z^{2} - 3 x y z^{2} - 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 |
|---|
| $(0:1:0)$, $(1:0:1)$, $(1:-1:1)$, $(1:0:0)$, $(-1:-1:1)$, $(1:1:0)$, $(0:0:1)$, $(0:-1:1)$ |
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{2985984x^{24}-71663616x^{23}z+859963392x^{22}z^{2}-6903595008x^{21}z^{3}+41690308608x^{20}z^{4}-201016442880x^{19}z^{5}+797998252032x^{18}z^{6}-2637579386880x^{17}z^{7}+7198870007808x^{16}z^{8}-15578284621824x^{15}z^{9}+23254556737536x^{14}z^{10}-7212656295936x^{13}z^{11}-88242814402560x^{12}z^{12}+322678760472576x^{11}z^{13}-574498257371136x^{10}z^{14}+92811310202880x^{9}z^{15}+2865144091078656x^{8}z^{16}-9501898696261632x^{7}z^{17}+13348487740391424x^{6}z^{18}+13120056787304448x^{5}z^{19}-117189055923904512x^{4}z^{20}+279949783612686336x^{3}z^{21}-2985244x^{2}y^{22}+11942616x^{2}y^{21}z-129794548x^{2}y^{20}z^{2}+529068912x^{2}y^{19}z^{3}-2129011524x^{2}y^{18}z^{4}+10735691000x^{2}y^{17}z^{5}-56397913996x^{2}y^{16}z^{6}+229448322880x^{2}y^{15}z^{7}-865319024024x^{2}y^{14}z^{8}+2520040341552x^{2}y^{13}z^{9}-6888217770120x^{2}y^{12}z^{10}+15246542191264x^{2}y^{11}z^{11}-24759988926600x^{2}y^{10}z^{12}-11245298122704x^{2}y^{9}z^{13}-17179015673240x^{2}y^{8}z^{14}-813962654904512x^{2}y^{7}z^{15}-210838776176524x^{2}y^{6}z^{16}+591083306394872x^{2}y^{5}z^{17}-13272851837035332x^{2}y^{4}z^{18}+59698440985998192x^{2}y^{3}z^{19}+274084107447844364x^{2}y^{2}z^{20}-189040787118343464x^{2}yz^{21}-288501866003238172x^{2}z^{22}-12xy^{23}-2977356xy^{22}z+1236684xy^{21}z^{2}+44976860xy^{20}z^{3}-1661643236xy^{19}z^{4}+6314705244xy^{18}z^{5}-10764188956xy^{17}z^{6}+17637657108xy^{16}z^{7}+24088093384xy^{15}z^{8}+153425003848xy^{14}z^{9}-225935611208xy^{13}z^{10}+2198595804504xy^{12}z^{11}-9808733970824xy^{11}z^{12}+41584237331960xy^{10}z^{13}+26369142990216xy^{9}z^{14}+605146542172648xy^{8}z^{15}+1659155311203972xy^{7}z^{16}+1566837956080196xy^{6}z^{17}+13752415963069244xy^{5}z^{18}-4587484317202036xy^{4}z^{19}-225560272735202772xy^{3}z^{20}-358573704266010772xy^{2}z^{21}+239295457838731988xyz^{22}+106150941926791748xz^{23}+y^{24}-2986012y^{23}z+9162796y^{22}z^{2}-139336892y^{21}z^{3}+1030714490y^{20}z^{4}-6062211460y^{19}z^{5}+16464115612y^{18}z^{6}-55663741988y^{17}z^{7}+182421629159y^{16}z^{8}-572424004632y^{15}z^{9}+1437048816088y^{14}z^{10}-3593590950232y^{13}z^{11}+6604818317708y^{12}z^{12}+10407532939384y^{11}z^{13}+16411308835864y^{10}z^{14}+230473939888184y^{9}z^{15}-357591575388385y^{8}z^{16}-1787625985837580y^{7}z^{17}-3268835007610116y^{6}z^{18}-46952419376322604y^{5}z^{19}-124058986232654054y^{4}z^{20}+26993573985335116y^{3}z^{21}+106150941926844236y^{2}z^{22}+8748yz^{23}+729z^{24}}{z(2985984x^{12}z^{11}-71663616x^{11}z^{12}+859963392x^{10}z^{13}-6831931392x^{9}z^{14}+39934550016x^{8}z^{15}-179517358080x^{7}z^{16}+623282356224x^{6}z^{17}-1586489131008x^{5}z^{18}+2278786535424x^{4}z^{19}+2622506139648x^{3}z^{20}-10x^{2}y^{21}-283x^{2}y^{20}z-4262x^{2}y^{19}z^{2}-46147x^{2}y^{18}z^{3}-395698x^{2}y^{17}z^{4}-2724764x^{2}y^{16}z^{5}-14761960x^{2}y^{15}z^{6}-60223628x^{2}y^{14}z^{7}-167243204x^{2}y^{13}z^{8}-190813818x^{2}y^{12}z^{9}+872427548x^{2}y^{11}z^{10}+6303701382x^{2}y^{10}z^{11}+22908441148x^{2}y^{9}z^{12}+57754398580x^{2}y^{8}z^{13}+112598638616x^{2}y^{7}z^{14}+113858817124x^{2}y^{6}z^{15}+118913431118x^{2}y^{5}z^{16}-918091588675x^{2}y^{4}z^{17}-415362322598x^{2}y^{3}z^{18}-7167137956123x^{2}y^{2}z^{19}-12811113529354x^{2}yz^{20}-8006665273344x^{2}z^{21}+11xy^{22}+289xy^{21}z+4020xy^{20}z^{2}+41262xy^{19}z^{3}+354237xy^{18}z^{4}+2590837xy^{17}z^{5}+15677568xy^{16}z^{6}+75627976xy^{15}z^{7}+278706526xy^{14}z^{8}+720121074xy^{13}z^{9}+897268744xy^{12}z^{10}-2260496204xy^{11}z^{11}-18018448502xy^{10}z^{12}-64329985214xy^{9}z^{13}-161831681248xy^{8}z^{14}-301869658488xy^{7}z^{15}-410972257753xy^{6}z^{16}-146966617043xy^{5}z^{17}+814916896932xy^{4}z^{18}+3368727434190xy^{3}z^{19}+14531350855977xy^{2}z^{20}+16966337200137xyz^{21}+4214202826752xz^{22}-y^{23}+3y^{22}z+538y^{21}z^{2}+9951y^{20}z^{3}+101277y^{19}z^{4}+668764y^{18}z^{5}+2775496y^{17}z^{6}+4017404y^{16}z^{7}-37797946y^{15}z^{8}-364052406y^{14}z^{9}-1847112884y^{13}z^{10}-6626252350y^{12}z^{11}-17920607830y^{11}z^{12}-36167748596y^{10}z^{13}-48090118104y^{9}z^{14}+1582436172y^{8}z^{15}+205271906795y^{7}z^{16}+925338577227y^{6}z^{17}+1884812825002y^{5}z^{18}+5462153036055y^{4}z^{19}+8537931546633y^{3}z^{20}+4214202826752y^{2}z^{21})}$ |
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 |
| 8.48.0-8.e.1.15 | $8$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.48.0-8.e.1.15 | $8$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
| 24.96.1-12.b.1.6 | $24$ | $2$ | $2$ | $1$ | $0$ | $2$ |
| 24.96.1-12.b.1.29 | $24$ | $2$ | $2$ | $1$ | $0$ | $2$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.384.5-24.ce.1.30 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.ce.2.27 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.ci.2.27 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.ci.4.21 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.cm.1.30 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.cm.2.27 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.cq.2.27 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.5-24.cq.4.21 | $24$ | $2$ | $2$ | $5$ | $0$ | $2$ |
| 24.384.7-24.g.2.5 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.i.1.30 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.n.2.16 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.p.1.12 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.x.2.6 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.y.1.21 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.bc.2.16 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 24.384.7-24.bd.2.8 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 24.384.7-24.bj.1.29 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bj.2.25 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bn.2.25 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bn.4.17 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.br.1.29 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.br.2.25 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bv.2.25 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bv.4.17 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bz.2.22 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.bz.4.14 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.cd.2.23 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.cd.4.15 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.ch.2.24 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.ch.4.16 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.cl.2.24 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.cl.4.16 | $24$ | $2$ | $2$ | $7$ | $0$ | $2^{2}$ |
| 24.384.7-24.cr.2.32 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 24.384.7-24.cs.2.28 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{2}\cdot2$ |
| 24.384.7-24.cw.2.23 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.cx.2.31 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.dg.2.32 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.di.1.30 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.dn.2.27 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.7-24.dp.2.21 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{2}\cdot2$ |
| 24.384.9-24.bs.1.8 | $24$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 24.384.9-24.by.2.11 | $24$ | $2$ | $2$ | $9$ | $0$ | $1^{4}\cdot2$ |
| 24.384.9-24.ck.2.22 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 24.384.9-24.cm.1.22 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 24.384.9-24.dz.2.8 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 24.384.9-24.ea.2.22 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2$ |
| 24.384.9-24.eh.2.12 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 24.384.9-24.ei.2.12 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2$ |
| 24.384.9-24.fd.2.31 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fd.4.31 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fh.2.30 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fh.4.30 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fl.1.27 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fl.3.27 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fp.2.26 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.384.9-24.fp.4.26 | $24$ | $2$ | $2$ | $9$ | $0$ | $2\cdot4$ |
| 24.576.13-24.bq.1.39 | $24$ | $3$ | $3$ | $13$ | $0$ | $1^{4}\cdot2^{3}$ |
| 120.384.5-120.ne.1.34 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ne.2.34 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ni.1.33 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ni.2.33 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.nm.1.33 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.nm.4.33 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.nq.1.35 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.nq.4.35 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.7-120.ck.1.9 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.cm.2.9 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.cs.2.3 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.cu.1.5 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.dj.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.dl.1.5 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.dr.1.3 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.dt.1.5 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ej.3.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ej.4.33 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.en.3.50 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.en.4.34 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.er.2.52 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.er.3.36 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ev.2.50 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ev.3.34 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.fp.2.52 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.fp.3.55 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ft.3.52 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ft.4.55 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.fx.3.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.fx.4.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.gb.3.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.gb.4.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.gt.2.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.gv.2.17 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.hb.2.33 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.hd.2.23 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.hr.2.49 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ht.2.21 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.hz.2.41 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.7-120.ib.2.19 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.384.9-120.jj.2.4 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.jl.2.34 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.jr.2.8 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.jt.2.49 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.kh.2.4 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.kj.2.34 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.kp.2.4 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.kr.2.49 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.ph.2.18 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.ph.3.18 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pl.3.38 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pl.4.42 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pp.3.40 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pp.4.44 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pt.3.20 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 120.384.9-120.pt.4.20 | $120$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.5-168.ne.1.44 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.ne.3.58 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.ni.1.46 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.ni.4.52 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.nm.1.46 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.nm.3.52 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.nq.1.44 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.5-168.nq.2.58 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 168.384.7-168.cf.2.7 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ch.2.18 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.cn.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.cp.2.56 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.dd.2.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.df.2.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.dl.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.dn.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ed.2.63 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ed.3.59 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.eh.2.63 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.eh.4.55 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.el.2.63 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.el.4.55 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ep.2.63 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ep.3.59 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fj.3.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fj.4.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fn.2.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fn.4.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fr.3.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fr.4.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fv.2.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.fv.4.54 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.gn.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.gp.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.gv.1.46 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.gx.2.44 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.hl.2.60 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.hn.2.56 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.ht.2.60 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.7-168.hv.2.48 | $168$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 168.384.9-168.jj.2.35 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.jl.2.7 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.jr.2.35 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.jt.2.35 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.kh.2.47 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.kj.2.43 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.kp.2.39 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.kr.2.47 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.ph.3.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.ph.4.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pl.2.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pl.4.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pp.3.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pp.4.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pt.2.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 168.384.9-168.pt.4.55 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.5-264.ne.1.43 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.ne.2.57 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.ni.1.39 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.ni.3.51 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.nm.1.45 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.nm.3.50 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.nq.1.42 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.5-264.nq.4.36 | $264$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 264.384.7-264.cf.2.19 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ch.2.2 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.cn.2.46 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.cp.2.46 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.dd.2.10 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.df.2.6 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.dl.2.56 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.dn.2.14 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ed.2.60 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ed.3.58 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.eh.2.56 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.eh.3.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.el.2.62 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.el.3.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ep.2.60 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ep.4.40 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fj.2.50 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fj.4.54 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fn.2.50 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fn.4.54 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fr.2.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fr.4.50 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fv.2.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.fv.4.50 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.gn.2.48 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.gp.2.40 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.gv.2.40 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.gx.2.56 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.hl.2.56 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.hn.2.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.ht.2.56 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.7-264.hv.2.52 | $264$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 264.384.9-264.jj.2.11 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.jl.2.11 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.jr.2.49 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.jt.2.49 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.kh.2.7 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.kj.2.35 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.kp.2.35 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.kr.2.35 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.ph.2.56 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.ph.4.56 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pl.2.56 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pl.4.56 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pp.2.52 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pp.4.52 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pt.2.52 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 264.384.9-264.pt.4.52 | $264$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.5-312.ne.1.53 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.ne.4.38 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.ni.1.59 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.ni.3.34 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.nm.1.51 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.nm.3.51 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.nq.1.55 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.nq.2.41 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.7-312.ck.2.7 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.cm.2.18 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.cs.2.10 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.cu.2.11 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.dj.2.18 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.dl.2.7 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.dr.2.7 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.dt.2.21 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ej.2.63 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ej.4.34 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.en.2.61 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.en.3.50 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.er.3.49 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.er.4.60 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ev.2.57 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ev.4.54 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.fp.2.55 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.fp.4.54 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ft.2.55 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ft.3.54 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.fx.3.53 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.fx.4.53 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.gb.3.53 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.gb.4.53 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.gt.2.57 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.gv.2.51 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.hb.2.53 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.hd.2.39 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.hr.2.36 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ht.2.55 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.hz.2.55 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.7-312.ib.2.38 | $312$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 312.384.9-312.jj.2.50 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.jl.2.4 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.jr.2.18 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.jt.2.34 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.kh.2.7 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.kj.2.36 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.kp.2.8 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.kr.2.25 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.ph.1.49 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.ph.4.49 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pl.1.49 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pl.3.25 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pp.1.43 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pp.4.51 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pt.1.51 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |
| 312.384.9-312.pt.4.43 | $312$ | $2$ | $2$ | $9$ | $?$ | not computed |