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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 42350bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.v1 | 42350bi1 | \([1, -1, 0, -2290492, 747310416]\) | \(384082046109/152649728\) | \(528180282784000000000\) | \([2]\) | \(1612800\) | \(2.6746\) | \(\Gamma_0(N)\)-optimal |
42350.v2 | 42350bi2 | \([1, -1, 0, 7389508, 5403390416]\) | \(12896863402851/11111230592\) | \(-38445747614832250000000\) | \([2]\) | \(3225600\) | \(3.0212\) |
Rank
sage: E.rank()
The elliptic curves in class 42350bi have rank \(1\).
Complex multiplication
The elliptic curves in class 42350bi do not have complex multiplication.Modular form 42350.2.a.bi
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.