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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 242550.en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.en1 | 242550en1 | \([1, -1, 0, -25635192, -49945006784]\) | \(37537160298467283/5519360000\) | \(273943343520000000000\) | \([2]\) | \(16515072\) | \(2.9359\) | \(\Gamma_0(N)\)-optimal |
| 242550.en2 | 242550en2 | \([1, -1, 0, -23283192, -59482366784]\) | \(-28124139978713043/14526050000000\) | \(-720973936314843750000000\) | \([2]\) | \(33030144\) | \(3.2824\) |
Rank
sage: E.rank()
The elliptic curves in class 242550.en have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.en do not have complex multiplication.Modular form 242550.2.a.en
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.
