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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 32490q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.w2 | 32490q1 | \([1, -1, 0, -2034, 36868]\) | \(-186169411/6480\) | \(-32401367280\) | \([2]\) | \(30720\) | \(0.78973\) | \(\Gamma_0(N)\)-optimal |
| 32490.w1 | 32490q2 | \([1, -1, 0, -32814, 2296120]\) | \(781484460931/900\) | \(4500189900\) | \([2]\) | \(61440\) | \(1.1363\) |
Rank
sage: E.rank()
The elliptic curves in class 32490q have rank \(1\).
Complex multiplication
The elliptic curves in class 32490q do not have complex multiplication.Modular form 32490.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
