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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 277350.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277350.x1 | 277350x4 | \([1, 1, 0, -1531010, -727411500]\) | \(502270291349/1889568\) | \(1493080666721604000\) | \([2]\) | \(6451200\) | \(2.3466\) | |
| 277350.x2 | 277350x2 | \([1, 1, 0, -98035, 11772475]\) | \(131872229/18\) | \(14223066860250\) | \([2]\) | \(1290240\) | \(1.5419\) | |
| 277350.x3 | 277350x3 | \([1, 1, 0, -51810, -21833100]\) | \(-19465109/248832\) | \(-196619676276096000\) | \([2]\) | \(3225600\) | \(2.0000\) | |
| 277350.x4 | 277350x1 | \([1, 1, 0, -5585, 216225]\) | \(-24389/12\) | \(-9482044573500\) | \([2]\) | \(645120\) | \(1.1953\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277350.x have rank \(1\).
Complex multiplication
The elliptic curves in class 277350.x do not have complex multiplication.Modular form 277350.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
