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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 182070.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182070.m1 | 182070dk7 | \([1, -1, 0, -34592951520, 2474623238424700]\) | \(260174968233082037895439009/223081361502731896500\) | \(3925403840040992298556544596500\) | \([2]\) | \(509607936\) | \(4.7971\) | |
| 182070.m2 | 182070dk8 | \([1, -1, 0, -22719386520, -1304109090794300]\) | \(73704237235978088924479009/899277423164136103500\) | \(15823944350937802938720723403500\) | \([2]\) | \(509607936\) | \(4.7971\) | |
| 182070.m3 | 182070dk5 | \([1, -1, 0, -22652436780, -1312256189579504]\) | \(73054578035931991395831649/136386452160\) | \(2399895264364678100160\) | \([2]\) | \(169869312\) | \(4.2478\) | |
| 182070.m4 | 182070dk6 | \([1, -1, 0, -2646169020, 20068877315200]\) | \(116454264690812369959009/57505157319440250000\) | \(1011877298234652331223390250000\) | \([2, 2]\) | \(254803968\) | \(4.4506\) | |
| 182070.m5 | 182070dk4 | \([1, -1, 0, -1486539180, -18340874520944]\) | \(20645800966247918737249/3688936444974392640\) | \(64911587365367212968616184640\) | \([2]\) | \(169869312\) | \(4.2478\) | |
| 182070.m6 | 182070dk2 | \([1, -1, 0, -1415791980, -20503290987824]\) | \(17836145204788591940449/770635366502400\) | \(13560321698605345157222400\) | \([2, 2]\) | \(84934656\) | \(3.9012\) | |
| 182070.m7 | 182070dk1 | \([1, -1, 0, -84079980, -353689400624]\) | \(-3735772816268612449/909650165760000\) | \(-16006466114940315893760000\) | \([2]\) | \(42467328\) | \(3.5547\) | \(\Gamma_0(N)\)-optimal |
| 182070.m8 | 182070dk3 | \([1, -1, 0, 605080980, 2406136565200]\) | \(1392333139184610040991/947901937500000000\) | \(-16679555299375514437500000000\) | \([2]\) | \(127401984\) | \(4.1040\) |
Rank
sage: E.rank()
The elliptic curves in class 182070.m have rank \(0\).
Complex multiplication
The elliptic curves in class 182070.m do not have complex multiplication.Modular form 182070.2.a.m
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
