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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 42432.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.bm1 | 42432u2 | \([0, 1, 0, -209, 207]\) | \(61918288/33813\) | \(553992192\) | \([2]\) | \(16384\) | \(0.36851\) | |
| 42432.bm2 | 42432u1 | \([0, 1, 0, 51, 51]\) | \(14047232/8619\) | \(-8825856\) | \([2]\) | \(8192\) | \(0.021933\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42432.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 42432.bm do not have complex multiplication.Modular form 42432.2.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 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.
