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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 430950.im
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.im1 | 430950im2 | \([1, 0, 0, -659188, 183445742]\) | \(420021471169/50191650\) | \(3785398561638281250\) | \([2]\) | \(8294400\) | \(2.2957\) | \(\Gamma_0(N)\)-optimal* |
430950.im2 | 430950im1 | \([1, 0, 0, 59062, 14656992]\) | \(302111711/1404540\) | \(-105928848638437500\) | \([2]\) | \(4147200\) | \(1.9492\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.im have rank \(0\).
Complex multiplication
The elliptic curves in class 430950.im do not have complex multiplication.Modular form 430950.2.a.im
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.