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SageMath
sage: E = EllipticCurve("v1")
sage: E.isogeny_class()
Elliptic curves in class 63525v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
63525.c2 | 63525v1 | [0, -1, 1, -27044508, -63385903582] | [] | 17280000 | \(\Gamma_0(N)\)-optimal |
63525.c1 | 63525v2 | [0, -1, 1, -81040758, 5308802648918] | [] | 86400000 |
Rank
sage: E.rank()
The elliptic curves in class 63525v have rank \(1\).
Complex multiplication
The elliptic curves in class 63525v do not have complex multiplication.Modular form 63525.2.a.v
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.