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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 414736j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 414736.j1 | 414736j1 | \([0, 1, 0, -23452, -1111860]\) | \(109744/23\) | \(298970912850176\) | \([2]\) | \(1622016\) | \(1.4924\) | \(\Gamma_0(N)\)-optimal |
| 414736.j2 | 414736j2 | \([0, 1, 0, 50608, -6651548]\) | \(275684/529\) | \(-27505323982216192\) | \([2]\) | \(3244032\) | \(1.8390\) |
Rank
sage: E.rank()
The elliptic curves in class 414736j have rank \(1\).
Complex multiplication
The elliptic curves in class 414736j do not have complex multiplication.Modular form 414736.2.a.j
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.
