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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 236992.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.bs1 | 236992bs2 | \([0, 0, 0, -2071564, -1147591440]\) | \(50668941906/1127\) | \(21867586768470016\) | \([2]\) | \(2162688\) | \(2.2503\) | |
| 236992.bs2 | 236992bs1 | \([0, 0, 0, -124844, -19272528]\) | \(-22180932/3703\) | \(-35925321119629312\) | \([2]\) | \(1081344\) | \(1.9037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 236992.bs do not have complex multiplication.Modular form 236992.2.a.bs
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.
