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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 38640.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.w1 | 38640bq1 | \([0, -1, 0, -4598536, -2384597264]\) | \(2625564132023811051529/918925030195200000\) | \(3763916923679539200000\) | \([2]\) | \(1728000\) | \(2.8414\) | \(\Gamma_0(N)\)-optimal |
| 38640.w2 | 38640bq2 | \([0, -1, 0, 13751544, -16682979600]\) | \(70213095586874240921591/69970703040000000000\) | \(-286599999651840000000000\) | \([2]\) | \(3456000\) | \(3.1880\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.w have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.w do not have complex multiplication.Modular form 38640.2.a.w
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.
