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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 58835.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58835.f1 | 58835a3 | \([0, -1, 1, -220771, -41693174]\) | \(-250523582464/13671875\) | \(-64942831419921875\) | \([]\) | \(388800\) | \(1.9842\) | |
| 58835.f2 | 58835a1 | \([0, -1, 1, -2241, 46056]\) | \(-262144/35\) | \(-166253648435\) | \([]\) | \(43200\) | \(0.88564\) | \(\Gamma_0(N)\)-optimal |
| 58835.f3 | 58835a2 | \([0, -1, 1, 14569, -120363]\) | \(71991296/42875\) | \(-203660719332875\) | \([]\) | \(129600\) | \(1.4349\) |
Rank
sage: E.rank()
The elliptic curves in class 58835.f have rank \(1\).
Complex multiplication
The elliptic curves in class 58835.f do not have complex multiplication.Modular form 58835.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
