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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 59850.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59850.u1 | 59850cn2 | \([1, -1, 0, -4887, -112379]\) | \(141665198597/20802264\) | \(1895606307000\) | \([2]\) | \(98304\) | \(1.0807\) | |
59850.u2 | 59850cn1 | \([1, -1, 0, 513, -9779]\) | \(163667323/536256\) | \(-48866328000\) | \([2]\) | \(49152\) | \(0.73417\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59850.u have rank \(1\).
Complex multiplication
The elliptic curves in class 59850.u do not have complex multiplication.Modular form 59850.2.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.