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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 422730.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 422730.o1 | 422730o1 | \([1, -1, 0, -2805, -36379]\) | \(3348743385681/1123146640\) | \(818773900560\) | \([2]\) | \(811008\) | \(0.98841\) | \(\Gamma_0(N)\)-optimal |
| 422730.o2 | 422730o2 | \([1, -1, 0, 8175, -258175]\) | \(82876153250799/86836726900\) | \(-63303973910100\) | \([2]\) | \(1622016\) | \(1.3350\) |
Rank
sage: E.rank()
The elliptic curves in class 422730.o have rank \(0\).
Complex multiplication
The elliptic curves in class 422730.o do not have complex multiplication.Modular form 422730.2.a.o
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.
