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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 59150bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59150.bh2 | 59150bi1 | \([1, 1, 1, 12587, -337719]\) | \(17303/14\) | \(-178441095218750\) | \([]\) | \(202176\) | \(1.4224\) | \(\Gamma_0(N)\)-optimal |
59150.bh1 | 59150bi2 | \([1, 1, 1, -262038, -52516469]\) | \(-156116857/2744\) | \(-34974454662875000\) | \([]\) | \(606528\) | \(1.9718\) |
Rank
sage: E.rank()
The elliptic curves in class 59150bi have rank \(0\).
Complex multiplication
The elliptic curves in class 59150bi do not have complex multiplication.Modular form 59150.2.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.