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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 457776.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 457776.n1 | 457776n1 | \([0, 0, 0, -604299, 186585914]\) | \(-1171657/44\) | \(-916498004695105536\) | \([]\) | \(7050240\) | \(2.2170\) | \(\Gamma_0(N)\)-optimal |
| 457776.n2 | 457776n2 | \([0, 0, 0, 2933061, 607531754]\) | \(133970183/85184\) | \(-1774340137089724317696\) | \([]\) | \(21150720\) | \(2.7663\) |
Rank
sage: E.rank()
The elliptic curves in class 457776.n have rank \(0\).
Complex multiplication
The elliptic curves in class 457776.n do not have complex multiplication.Modular form 457776.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
