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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 88400bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88400.y2 | 88400bi1 | \([0, 0, 0, -293075, -60968750]\) | \(43499078731809/82055753\) | \(5251568192000000\) | \([2]\) | \(614400\) | \(1.9065\) | \(\Gamma_0(N)\)-optimal |
88400.y1 | 88400bi2 | \([0, 0, 0, -4687075, -3905718750]\) | \(177930109857804849/634933\) | \(40635712000000\) | \([2]\) | \(1228800\) | \(2.2530\) |
Rank
sage: E.rank()
The elliptic curves in class 88400bi have rank \(1\).
Complex multiplication
The elliptic curves in class 88400bi do not have complex multiplication.Modular form 88400.2.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.