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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 93925.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93925.s1 | 93925f2 | \([1, -1, 0, -84660292, 299846105991]\) | \(177930109857804849/634933\) | \(239464673404328125\) | \([2]\) | \(5529600\) | \(2.9765\) | |
| 93925.s2 | 93925f1 | \([1, -1, 0, -5293667, 4681627616]\) | \(43499078731809/82055753\) | \(30947287498194640625\) | \([2]\) | \(2764800\) | \(2.6299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93925.s have rank \(0\).
Complex multiplication
The elliptic curves in class 93925.s do not have complex multiplication.Modular form 93925.2.a.s
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.
