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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 38640.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.cu1 | 38640cx2 | \([0, 1, 0, -11800, -3052]\) | \(44365623586201/25674468750\) | \(105162624000000\) | \([2]\) | \(110592\) | \(1.3800\) | |
38640.cu2 | 38640cx1 | \([0, 1, 0, -8120, 278100]\) | \(14457238157881/49990500\) | \(204761088000\) | \([2]\) | \(55296\) | \(1.0334\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.cu do not have complex multiplication.Modular form 38640.2.a.cu
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.