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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 63426.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63426.u1 | 63426v2 | \([1, 1, 1, -98953229, 73424872451]\) | \(120737856347074599697/67244278190817024\) | \(59679544420538129197465344\) | \([2]\) | \(20643840\) | \(3.6363\) | |
63426.u2 | 63426v1 | \([1, 1, 1, -60820749, -181559394813]\) | \(28035534600833657617/183328572506112\) | \(162704782931649794998272\) | \([2]\) | \(10321920\) | \(3.2897\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63426.u have rank \(1\).
Complex multiplication
The elliptic curves in class 63426.u do not have complex multiplication.Modular form 63426.2.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.