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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 49725q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 49725.i2 | 49725q1 | \([1, -1, 1, -7430, 235572]\) | \(3981876625/232713\) | \(2650746515625\) | \([2]\) | \(73728\) | \(1.1373\) | \(\Gamma_0(N)\)-optimal |
| 49725.i1 | 49725q2 | \([1, -1, 1, -22055, -963678]\) | \(104154702625/24649677\) | \(280775227078125\) | \([2]\) | \(147456\) | \(1.4839\) |
Rank
sage: E.rank()
The elliptic curves in class 49725q have rank \(0\).
Complex multiplication
The elliptic curves in class 49725q do not have complex multiplication.Modular form 49725.2.a.q
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 Cremona 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 Cremona labels.
