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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6042.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6042.n1 | 6042n2 | \([1, 0, 0, -899, -8979]\) | \(80358714342577/12253768116\) | \(12253768116\) | \([]\) | \(6048\) | \(0.65953\) | |
6042.n2 | 6042n1 | \([1, 0, 0, -239, 1401]\) | \(1510187880817/1740096\) | \(1740096\) | \([3]\) | \(2016\) | \(0.11022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6042.n have rank \(0\).
Complex multiplication
The elliptic curves in class 6042.n do not have complex multiplication.Modular form 6042.2.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.