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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 162450bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.ee2 | 162450bi1 | \([1, -1, 1, 120145, 47383647]\) | \(129205871/729000\) | \(-1082155040015625000\) | \([]\) | \(2488320\) | \(2.1425\) | \(\Gamma_0(N)\)-optimal |
| 162450.ee1 | 162450bi2 | \([1, -1, 1, -7190105, 7430736147]\) | \(-27692833539889/35156250\) | \(-52187260803222656250\) | \([]\) | \(7464960\) | \(2.6918\) |
Rank
sage: E.rank()
The elliptic curves in class 162450bi have rank \(1\).
Complex multiplication
The elliptic curves in class 162450bi do not have complex multiplication.Modular form 162450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
