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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 67830.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67830.n1 | 67830n2 | \([1, 0, 1, -28939, 1892342]\) | \(2680110489192084649/70150328640\) | \(70150328640\) | \([2]\) | \(175104\) | \(1.1872\) | |
67830.n2 | 67830n1 | \([1, 0, 1, -1739, 31862]\) | \(-581116772167849/106270617600\) | \(-106270617600\) | \([2]\) | \(87552\) | \(0.84061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67830.n have rank \(1\).
Complex multiplication
The elliptic curves in class 67830.n do not have complex multiplication.Modular form 67830.2.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.