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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 165649.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
165649.n1 | 165649n2 | \([0, 1, 1, -431073914, -3445036543877]\) | \(38477541376\) | \(230235149713106405197\) | \([]\) | \(35964000\) | \(3.4226\) | |
165649.n2 | 165649n1 | \([0, 1, 1, -2043004, 853919061]\) | \(4096\) | \(230235149713106405197\) | \([]\) | \(7192800\) | \(2.6178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 165649.n have rank \(1\).
Complex multiplication
The elliptic curves in class 165649.n do not have complex multiplication.Modular form 165649.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.