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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 481338.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 481338.bv1 | 481338bv1 | \([1, -1, 0, -42969240, 92853995328]\) | \(6793805286030262681/1048227429629952\) | \(1353752149594284531007488\) | \([2]\) | \(144506880\) | \(3.3538\) | \(\Gamma_0(N)\)-optimal |
| 481338.bv2 | 481338bv2 | \([1, -1, 0, 74817000, 512290795968]\) | \(35862531227445945959/108547797844556928\) | \(-140186004021732513509039232\) | \([2]\) | \(289013760\) | \(3.7004\) |
Rank
sage: E.rank()
The elliptic curves in class 481338.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 481338.bv do not have complex multiplication.Modular form 481338.2.a.bv
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.
