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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 86190n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.m2 | 86190n1 | \([1, 1, 0, 2363, 118201]\) | \(302111711/1404540\) | \(-6779446312860\) | \([2]\) | \(172800\) | \(1.1445\) | \(\Gamma_0(N)\)-optimal |
86190.m1 | 86190n2 | \([1, 1, 0, -26367, 1457019]\) | \(420021471169/50191650\) | \(242265507944850\) | \([2]\) | \(345600\) | \(1.4910\) |
Rank
sage: E.rank()
The elliptic curves in class 86190n have rank \(0\).
Complex multiplication
The elliptic curves in class 86190n do not have complex multiplication.Modular form 86190.2.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 Cremona 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 Cremona labels.