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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 32340.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.bn1 | 32340bi2 | \([0, 1, 0, -19424890, -32961887155]\) | \(-8788102954619113216/954968814855\) | \(-88083282861518701680\) | \([]\) | \(1959552\) | \(2.8570\) | |
| 32340.bn2 | 32340bi1 | \([0, 1, 0, 23210, -137383975]\) | \(14990845184/88418496375\) | \(-8155440581137542000\) | \([3]\) | \(653184\) | \(2.3077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 32340.bn do not have complex multiplication.Modular form 32340.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
