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SageMath
E = EllipticCurve("lu1")
E.isogeny_class()
Elliptic curves in class 221760lu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.df2 | 221760lu1 | \([0, 0, 0, -768, -25688]\) | \(-67108864/343035\) | \(-256074255360\) | \([2]\) | \(245760\) | \(0.87338\) | \(\Gamma_0(N)\)-optimal |
| 221760.df1 | 221760lu2 | \([0, 0, 0, -18588, -973712]\) | \(59466754384/121275\) | \(1448500838400\) | \([2]\) | \(491520\) | \(1.2199\) |
Rank
sage: E.rank()
The elliptic curves in class 221760lu have rank \(1\).
Complex multiplication
The elliptic curves in class 221760lu do not have complex multiplication.Modular form 221760.2.a.lu
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 Cremona 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 Cremona labels.
