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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 227850.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227850.bi1 | 227850iy2 | \([1, 1, 0, -809750, 280125000]\) | \(31942518433489/27900\) | \(51287610937500\) | \([2]\) | \(2764800\) | \(1.9311\) | |
227850.bi2 | 227850iy1 | \([1, 1, 0, -50250, 4426500]\) | \(-7633736209/230640\) | \(-423977583750000\) | \([2]\) | \(1382400\) | \(1.5845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227850.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 227850.bi do not have complex multiplication.Modular form 227850.2.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 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.