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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 435120.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.u1 | 435120u2 | \([0, -1, 0, -66656, 2164800]\) | \(198155287/102675\) | \(16970983828377600\) | \([2]\) | \(2064384\) | \(1.8062\) | \(\Gamma_0(N)\)-optimal* |
435120.u2 | 435120u1 | \([0, -1, 0, 15664, 254976]\) | \(2571353/1665\) | \(-275205143162880\) | \([2]\) | \(1032192\) | \(1.4596\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.u have rank \(1\).
Complex multiplication
The elliptic curves in class 435120.u do not have complex multiplication.Modular form 435120.2.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.