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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 20160.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.fl1 | 20160fl2 | \([0, 0, 0, -49332, 4217344]\) | \(4446542056384/25725\) | \(76814438400\) | \([2]\) | \(61440\) | \(1.2791\) | |
20160.fl2 | 20160fl1 | \([0, 0, 0, -3027, 68416]\) | \(-65743598656/5294205\) | \(-247006428480\) | \([2]\) | \(30720\) | \(0.93250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20160.fl have rank \(1\).
Complex multiplication
The elliptic curves in class 20160.fl do not have complex multiplication.Modular form 20160.2.a.fl
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.