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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 468270j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.j2 | 468270j1 | \([1, -1, 0, -7990560, 8700466176]\) | \(-43688964783576601/26658734080\) | \(-34428901158408683520\) | \([2]\) | \(19491840\) | \(2.6919\) | \(\Gamma_0(N)\)-optimal* |
468270.j1 | 468270j2 | \([1, -1, 0, -127867680, 556562880000]\) | \(179028606517430416921/66598400\) | \(86009700386649600\) | \([2]\) | \(38983680\) | \(3.0384\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270j have rank \(1\).
Complex multiplication
The elliptic curves in class 468270j do not have complex multiplication.Modular form 468270.2.a.j
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 Cremona 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 Cremona labels.