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SageMath
E = EllipticCurve("jm1")
E.isogeny_class()
Elliptic curves in class 142800.jm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.jm1 | 142800cb2 | \([0, 1, 0, -21619008, -36897288012]\) | \(17460273607244690041/918397653311250\) | \(58777449811920000000000\) | \([2]\) | \(17694720\) | \(3.1260\) | |
| 142800.jm2 | 142800cb1 | \([0, 1, 0, 880992, -2292288012]\) | \(1181569139409959/36161310937500\) | \(-2314323900000000000000\) | \([2]\) | \(8847360\) | \(2.7795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.jm have rank \(0\).
Complex multiplication
The elliptic curves in class 142800.jm do not have complex multiplication.Modular form 142800.2.a.jm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
