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SageMath
E = EllipticCurve("jc1")
E.isogeny_class()
Elliptic curves in class 221760.jc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.jc1 | 221760bw1 | \([0, 0, 0, -4332, 107984]\) | \(188183524/3465\) | \(165542952960\) | \([2]\) | \(294912\) | \(0.94733\) | \(\Gamma_0(N)\)-optimal |
| 221760.jc2 | 221760bw2 | \([0, 0, 0, -12, 313616]\) | \(-2/444675\) | \(-42489357926400\) | \([2]\) | \(589824\) | \(1.2939\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.jc have rank \(1\).
Complex multiplication
The elliptic curves in class 221760.jc do not have complex multiplication.Modular form 221760.2.a.jc
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.
