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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 169050bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.ia1 | 169050bi1 | \([1, 0, 0, -352075438, -1598550096508]\) | \(2625564132023811051529/918925030195200000\) | \(1689228294959923200000000000\) | \([2]\) | \(82944000\) | \(3.9259\) | \(\Gamma_0(N)\)-optimal |
169050.ia2 | 169050bi2 | \([1, 0, 0, 1052852562, -11173134416508]\) | \(70213095586874240921591/69970703040000000000\) | \(-128624738155515000000000000000\) | \([2]\) | \(165888000\) | \(4.2725\) |
Rank
sage: E.rank()
The elliptic curves in class 169050bi have rank \(1\).
Complex multiplication
The elliptic curves in class 169050bi do not have complex multiplication.Modular form 169050.2.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.