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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 296240.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296240.di1 | 296240di4 | \([0, -1, 0, -1412057760, -20422804321408]\) | \(513516182162686336369/1944885031250\) | \(1179290765737519232000000\) | \([2]\) | \(189775872\) | \(3.8335\) | |
| 296240.di2 | 296240di3 | \([0, -1, 0, -89557760, -309166321408]\) | \(131010595463836369/7704101562500\) | \(4671420513284000000000000\) | \([2]\) | \(94887936\) | \(3.4869\) | |
| 296240.di3 | 296240di2 | \([0, -1, 0, -24046400, -4852748800]\) | \(2535986675931409/1450751712200\) | \(879670556400841301196800\) | \([2]\) | \(63258624\) | \(3.2842\) | |
| 296240.di4 | 296240di1 | \([0, -1, 0, -15582400, 23579520000]\) | \(690080604747409/3406760000\) | \(2065705964378685440000\) | \([2]\) | \(31629312\) | \(2.9376\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296240.di have rank \(1\).
Complex multiplication
The elliptic curves in class 296240.di do not have complex multiplication.Modular form 296240.2.a.di
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
