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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 47610.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.f1 | 47610a2 | \([1, -1, 0, -3155055, 506242825]\) | \(71421719949/39062500\) | \(1899653197636757812500\) | \([2]\) | \(2119680\) | \(2.7737\) | |
47610.f2 | 47610a1 | \([1, -1, 0, -2425035, 1452202741]\) | \(32431240269/50000\) | \(2431556092975050000\) | \([2]\) | \(1059840\) | \(2.4272\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47610.f have rank \(0\).
Complex multiplication
The elliptic curves in class 47610.f do not have complex multiplication.Modular form 47610.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.