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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5586.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.n1 | 5586q2 | \([1, 0, 1, -93861, 7699024]\) | \(2266158235375/675584064\) | \(27262253814118848\) | \([2]\) | \(43008\) | \(1.8592\) | |
5586.n2 | 5586q1 | \([1, 0, 1, 15899, 806096]\) | \(11015140625/13307904\) | \(-537021928009728\) | \([2]\) | \(21504\) | \(1.5126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5586.n have rank \(1\).
Complex multiplication
The elliptic curves in class 5586.n do not have complex multiplication.Modular form 5586.2.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.