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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 3630.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3630.u1 | 3630v2 | \([1, 0, 0, -1738591, -644446879]\) | \(2711280982499089/732421875000\) | \(157001133544921875000\) | \([]\) | \(142560\) | \(2.5833\) | |
3630.u2 | 3630v1 | \([1, 0, 0, -620551, 188045705]\) | \(123286270205329/43200000\) | \(9260303659200000\) | \([3]\) | \(47520\) | \(2.0340\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3630.u have rank \(0\).
Complex multiplication
The elliptic curves in class 3630.u do not have complex multiplication.Modular form 3630.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.