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SageMath
sage: E = EllipticCurve("54.b1")
sage: E.isogeny_class()
Elliptic curves in class 54.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
54.b1 | 54b2 | [1, -1, 1, -29, -53] | [] | 6 | |
54.b2 | 54b3 | [1, -1, 1, -14, 29] | [9] | 6 | |
54.b3 | 54b1 | [1, -1, 1, 1, -1] | [3] | 2 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54.b have rank \(0\).
Modular form 54.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.