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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 332592.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 332592.bn1 | 332592bn1 | \([0, -1, 0, -27941, -1911027]\) | \(-122023936/9963\) | \(-196974584082432\) | \([]\) | \(1536000\) | \(1.4889\) | \(\Gamma_0(N)\)-optimal |
| 332592.bn2 | 332592bn2 | \([0, -1, 0, 53179, 126015213]\) | \(841232384/347568603\) | \(-6871643181374779392\) | \([]\) | \(7680000\) | \(2.2936\) |
Rank
sage: E.rank()
The elliptic curves in class 332592.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 332592.bn do not have complex multiplication.Modular form 332592.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
