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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 18810.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18810.n1 | 18810j2 | \([1, -1, 0, -540654, 153147860]\) | \(23974794703037459169/101657600\) | \(74108390400\) | \([2]\) | \(194560\) | \(1.7164\) | |
18810.n2 | 18810j1 | \([1, -1, 0, -33774, 2401748]\) | \(-5844547788286689/12053381120\) | \(-8786914836480\) | \([2]\) | \(97280\) | \(1.3698\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18810.n have rank \(0\).
Complex multiplication
The elliptic curves in class 18810.n do not have complex multiplication.Modular form 18810.2.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.