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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 379050bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.bi2 | 379050bi1 | \([1, 1, 0, -262815, -97319835]\) | \(-1706927698345/2483133408\) | \(-2920529970497311200\) | \([]\) | \(8640000\) | \(2.2352\) | \(\Gamma_0(N)\)-optimal |
379050.bi1 | 379050bi2 | \([1, 1, 0, -5645325, 11713195875]\) | \(-43308090025/103996158\) | \(-47779207751222636718750\) | \([]\) | \(43200000\) | \(3.0399\) |
Rank
sage: E.rank()
The elliptic curves in class 379050bi have rank \(1\).
Complex multiplication
The elliptic curves in class 379050bi do not have complex multiplication.Modular form 379050.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.