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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 87360i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.h1 | 87360i1 | \([0, -1, 0, -131521, 18402241]\) | \(959781554388721/19377540\) | \(5079705845760\) | \([2]\) | \(368640\) | \(1.5583\) | \(\Gamma_0(N)\)-optimal |
| 87360.h2 | 87360i2 | \([0, -1, 0, -127041, 19709505]\) | \(-865005601073041/136840035150\) | \(-35871794174361600\) | \([2]\) | \(737280\) | \(1.9049\) |
Rank
sage: E.rank()
The elliptic curves in class 87360i have rank \(2\).
Complex multiplication
The elliptic curves in class 87360i do not have complex multiplication.Modular form 87360.2.a.i
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.
