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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 439824.fs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439824.fs1 | 439824fs2 | \([0, 1, 0, -961592, -209908140]\) | \(204055591784617/78708537864\) | \(37928881238678470656\) | \([2]\) | \(11612160\) | \(2.4559\) | |
439824.fs2 | 439824fs1 | \([0, 1, 0, -428472, 105485652]\) | \(18052771191337/444958272\) | \(214421076961394688\) | \([2]\) | \(5806080\) | \(2.1093\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439824.fs have rank \(1\).
Complex multiplication
The elliptic curves in class 439824.fs do not have complex multiplication.Modular form 439824.2.a.fs
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.