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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 123840.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.ej1 | 123840ba2 | \([0, 0, 0, -2891052, 1828633104]\) | \(4143336389555544/158034076225\) | \(101927640181528166400\) | \([2]\) | \(3538944\) | \(2.6073\) | |
| 123840.ej2 | 123840ba1 | \([0, 0, 0, -2864052, 1865601504]\) | \(32226650420588352/49691875\) | \(4006236879360000\) | \([2]\) | \(1769472\) | \(2.2607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 123840.ej have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.ej do not have complex multiplication.Modular form 123840.2.a.ej
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.
