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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 66240.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.u1 | 66240b2 | \([0, 0, 0, -5868, -173008]\) | \(12628458252/575\) | \(1017446400\) | \([2]\) | \(40960\) | \(0.80438\) | |
66240.u2 | 66240b1 | \([0, 0, 0, -348, -2992]\) | \(-10536048/2645\) | \(-1170063360\) | \([2]\) | \(20480\) | \(0.45780\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.u have rank \(1\).
Complex multiplication
The elliptic curves in class 66240.u do not have complex multiplication.Modular form 66240.2.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.