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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 215475bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215475.y2 | 215475bi1 | \([0, -1, 1, -22533, -2255407]\) | \(-2835349504/3316275\) | \(-1479939535546875\) | \([]\) | \(787968\) | \(1.6049\) | \(\Gamma_0(N)\)-optimal |
| 215475.y1 | 215475bi2 | \([0, -1, 1, -2177283, -1235849782]\) | \(-2557850287243264/796875\) | \(-355617919921875\) | \([]\) | \(2363904\) | \(2.1543\) |
Rank
sage: E.rank()
The elliptic curves in class 215475bi have rank \(1\).
Complex multiplication
The elliptic curves in class 215475bi do not have complex multiplication.Modular form 215475.2.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.
