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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 169338q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169338.j2 | 169338q1 | \([1, 0, 1, -446, 1640]\) | \(57868344625/26296488\) | \(4444106472\) | \([]\) | \(72576\) | \(0.54630\) | \(\Gamma_0(N)\)-optimal |
169338.j1 | 169338q2 | \([1, 0, 1, -17996, -930616]\) | \(3813557241924625/251503002\) | \(42504007338\) | \([]\) | \(217728\) | \(1.0956\) |
Rank
sage: E.rank()
The elliptic curves in class 169338q have rank \(1\).
Complex multiplication
The elliptic curves in class 169338q do not have complex multiplication.Modular form 169338.2.a.q
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.