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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 22218.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22218.n1 | 22218n2 | \([1, 0, 1, -190716, -31580654]\) | \(5182207647625/91449288\) | \(13537776647497032\) | \([2]\) | \(202752\) | \(1.8916\) | |
22218.n2 | 22218n1 | \([1, 0, 1, -276, -1414958]\) | \(-15625/5842368\) | \(-864880140745152\) | \([2]\) | \(101376\) | \(1.5450\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22218.n have rank \(0\).
Complex multiplication
The elliptic curves in class 22218.n do not have complex multiplication.Modular form 22218.2.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.