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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 209484bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.j2 | 209484bm1 | \([0, 0, 0, -76176, -3954275]\) | \(764411904/336743\) | \(21535221327635664\) | \([2]\) | \(1622016\) | \(1.8298\) | \(\Gamma_0(N)\)-optimal |
| 209484.j1 | 209484bm2 | \([0, 0, 0, -1036311, -405866786]\) | \(120288273264/64009\) | \(65495549161734912\) | \([2]\) | \(3244032\) | \(2.1764\) |
Rank
sage: E.rank()
The elliptic curves in class 209484bm have rank \(1\).
Complex multiplication
The elliptic curves in class 209484bm do not have complex multiplication.Modular form 209484.2.a.bm
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 Cremona 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 Cremona labels.
