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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 247962.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.u1 | 247962u2 | \([1, 1, 1, -17635, -901099]\) | \(25128011089/245388\) | \(5923069781772\) | \([2]\) | \(1576960\) | \(1.2702\) | |
247962.u2 | 247962u1 | \([1, 1, 1, -295, -34099]\) | \(-117649/20592\) | \(-497040820848\) | \([2]\) | \(788480\) | \(0.92366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 247962.u have rank \(0\).
Complex multiplication
The elliptic curves in class 247962.u do not have complex multiplication.Modular form 247962.2.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.