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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 364650.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.n1 | 364650n2 | \([1, 1, 0, -500450, -103202460]\) | \(554456067209509140625/137563834142543952\) | \(3439095853563598800\) | \([]\) | \(8584704\) | \(2.2671\) | |
364650.n2 | 364650n1 | \([1, 1, 0, -170450, 27004980]\) | \(21906787790209140625/9401385996288\) | \(235034649907200\) | \([]\) | \(2861568\) | \(1.7178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.n have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.n do not have complex multiplication.Modular form 364650.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.