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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2850.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2850.b1 | 2850c2 | \([1, 1, 0, -583150, -171646250]\) | \(1403607530712116449/39475350\) | \(616802343750\) | \([2]\) | \(26880\) | \(1.7728\) | |
2850.b2 | 2850c1 | \([1, 1, 0, -36400, -2700500]\) | \(-341370886042369/1817528220\) | \(-28398878437500\) | \([2]\) | \(13440\) | \(1.4262\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.b have rank \(0\).
Complex multiplication
The elliptic curves in class 2850.b do not have complex multiplication.Modular form 2850.2.a.b
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 LMFDB 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 LMFDB labels.