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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 15600bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.d2 | 15600bm1 | \([0, -1, 0, -5684848, 5717413312]\) | \(-198417696411528597145/22989483914821632\) | \(-2354123152877735116800\) | \([]\) | \(806400\) | \(2.8372\) | \(\Gamma_0(N)\)-optimal |
| 15600.d1 | 15600bm2 | \([0, -1, 0, -3646500208, 84755659198912]\) | \(-134057911417971280740025/1872\) | \(-74880000000000\) | \([]\) | \(4032000\) | \(3.6419\) |
Rank
sage: E.rank()
The elliptic curves in class 15600bm have rank \(1\).
Complex multiplication
The elliptic curves in class 15600bm do not have complex multiplication.Modular form 15600.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
