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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 297920.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297920.n1 | 297920n1 | \([0, 1, 0, -180581, 27486619]\) | \(5405726654464/407253125\) | \(49062833052800000\) | \([2]\) | \(2764800\) | \(1.9479\) | \(\Gamma_0(N)\)-optimal |
| 297920.n2 | 297920n2 | \([0, 1, 0, 173199, 122370415]\) | \(298091207216/3525390625\) | \(-6795406240000000000\) | \([2]\) | \(5529600\) | \(2.2945\) |
Rank
sage: E.rank()
The elliptic curves in class 297920.n have rank \(0\).
Complex multiplication
The elliptic curves in class 297920.n do not have complex multiplication.Modular form 297920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
