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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 465690.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
465690.u1 | 465690u2 | \([1, 0, 1, -482304, -128960948]\) | \(263732349218689/4160250\) | \(195722626430250\) | \([2]\) | \(4105728\) | \(1.8762\) | |
465690.u2 | 465690u1 | \([1, 0, 1, -31054, -1888948]\) | \(70393838689/8062500\) | \(379307415562500\) | \([2]\) | \(2052864\) | \(1.5297\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 465690.u have rank \(1\).
Complex multiplication
The elliptic curves in class 465690.u do not have complex multiplication.Modular form 465690.2.a.u
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.