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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 203280.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.f1 | 203280dy2 | \([0, -1, 0, -63686, 6224715]\) | \(-121947169848064/397065375\) | \(-93014946486000\) | \([]\) | \(933120\) | \(1.5462\) | |
203280.f2 | 203280dy1 | \([0, -1, 0, 1654, 43551]\) | \(2134896896/4822335\) | \(-1129660907760\) | \([]\) | \(311040\) | \(0.99685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.f have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.f do not have complex multiplication.Modular form 203280.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.