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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 394944.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 394944.bc1 | 394944bc2 | \([0, -1, 0, -1409569, -643635551]\) | \(666940371553/37026\) | \(17195025717264384\) | \([2]\) | \(4423680\) | \(2.1807\) | |
| 394944.bc2 | 394944bc1 | \([0, -1, 0, -93089, -8828895]\) | \(192100033/38148\) | \(17716087102636032\) | \([2]\) | \(2211840\) | \(1.8341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 394944.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 394944.bc do not have complex multiplication.Modular form 394944.2.a.bc
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.
