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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 14490.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.n1 | 14490b1 | \([1, -1, 0, -1275, -16875]\) | \(8493409990827/185150000\) | \(4999050000\) | \([2]\) | \(10240\) | \(0.64932\) | \(\Gamma_0(N)\)-optimal |
14490.n2 | 14490b2 | \([1, -1, 0, 105, -52479]\) | \(4716275733/44023437500\) | \(-1188632812500\) | \([2]\) | \(20480\) | \(0.99590\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.n have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.n do not have complex multiplication.Modular form 14490.2.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.