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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 333795.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333795.n1 | 333795n2 | \([1, 1, 1, -99390421, 380275104518]\) | \(22100929481998139979094433/71639755865687411325\) | \(351966120568122251839725\) | \([2]\) | \(74280960\) | \(3.3840\) | |
333795.n2 | 333795n1 | \([1, 1, 1, -3565076, 11040885164]\) | \(-1019960453167729894673/10131394987524330135\) | \(-49775543573707033953255\) | \([2]\) | \(37140480\) | \(3.0374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333795.n have rank \(0\).
Complex multiplication
The elliptic curves in class 333795.n do not have complex multiplication.Modular form 333795.2.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.