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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 349830.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349830.a1 | 349830a2 | \([1, -1, 0, -1146105, 209629525]\) | \(47316161414809/22001657400\) | \(77418194707909481400\) | \([2]\) | \(12644352\) | \(2.5108\) | |
| 349830.a2 | 349830a1 | \([1, -1, 0, 253215, 24639421]\) | \(510273943271/370215360\) | \(-1302692988226368960\) | \([2]\) | \(6322176\) | \(2.1643\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 349830.a have rank \(0\).
Complex multiplication
The elliptic curves in class 349830.a do not have complex multiplication.Modular form 349830.2.a.a
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.
