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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 350658e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.e2 | 350658e1 | \([1, -1, 0, -339246, -66462984]\) | \(3343374301177/453439756\) | \(585602920745175564\) | \([]\) | \(5875200\) | \(2.1365\) | \(\Gamma_0(N)\)-optimal |
| 350658.e1 | 350658e2 | \([1, -1, 0, -26513361, -52540053219]\) | \(1596005697643892137/5553856\) | \(7172627128438464\) | \([]\) | \(17625600\) | \(2.6858\) |
Rank
sage: E.rank()
The elliptic curves in class 350658e have rank \(1\).
Complex multiplication
The elliptic curves in class 350658e do not have complex multiplication.Modular form 350658.2.a.e
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.
