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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 57330.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57330.cu1 | 57330cx2 | \([1, -1, 0, -5378004, -3157089440]\) | \(584759426925367/191909250000\) | \(5645544001086102750000\) | \([2]\) | \(3440640\) | \(2.8768\) | |
57330.cu2 | 57330cx1 | \([1, -1, 0, -2167524, 1191826768]\) | \(38282975119927/1314144000\) | \(38659198427190432000\) | \([2]\) | \(1720320\) | \(2.5302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57330.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 57330.cu do not have complex multiplication.Modular form 57330.2.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.