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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 308550.fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.fy1 | 308550fy2 | \([1, 1, 1, -550613, -157481719]\) | \(666940371553/37026\) | \(1024903399781250\) | \([2]\) | \(2949120\) | \(1.9457\) | |
308550.fy2 | 308550fy1 | \([1, 1, 1, -36363, -2178219]\) | \(192100033/38148\) | \(1055961078562500\) | \([2]\) | \(1474560\) | \(1.5991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.fy have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.fy do not have complex multiplication.Modular form 308550.2.a.fy
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.