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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 65366.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65366.n1 | 65366n2 | \([1, 1, 0, -26534, 1516880]\) | \(17561807821657/1590616244\) | \(187134410490356\) | \([2]\) | \(245760\) | \(1.4780\) | |
65366.n2 | 65366n1 | \([1, 1, 0, 1886, 112932]\) | \(6300872423/49827568\) | \(-5862163547632\) | \([2]\) | \(122880\) | \(1.1314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65366.n have rank \(1\).
Complex multiplication
The elliptic curves in class 65366.n do not have complex multiplication.Modular form 65366.2.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.