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SageMath
sage: E = EllipticCurve("53900.b1")
sage: E.isogeny_class()
Elliptic curves in class 53900.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 53900.b1 | 53900o4 | [0, 1, 0, -8697908, 9870581188] | [2] | 1492992 | |
| 53900.b2 | 53900o3 | [0, 1, 0, -545533, 152950188] | [2] | 746496 | |
| 53900.b3 | 53900o2 | [0, 1, 0, -122908, 9331188] | [2] | 497664 | |
| 53900.b4 | 53900o1 | [0, 1, 0, -55533, -4952312] | [2] | 248832 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53900.b have rank \(1\).
Modular form 53900.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
