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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 221760.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.di1 | 221760dq3 | \([0, 0, 0, -1722665388, 27420217431248]\) | \(2958414657792917260183849/12401051653985258880\) | \(2369877876606305232098426880\) | \([2]\) | \(154140672\) | \(4.1074\) | |
| 221760.di2 | 221760dq2 | \([0, 0, 0, -161474988, -44868561712]\) | \(2436531580079063806249/1405478914998681600\) | \(268591203361499089836441600\) | \([2, 2]\) | \(77070336\) | \(3.7608\) | |
| 221760.di3 | 221760dq1 | \([0, 0, 0, -114289068, -469107731248]\) | \(863913648706111516969/2486234429521920\) | \(475126798515301169233920\) | \([2]\) | \(38535168\) | \(3.4142\) | \(\Gamma_0(N)\)-optimal |
| 221760.di4 | 221760dq4 | \([0, 0, 0, 644740692, -358647704368]\) | \(155099895405729262880471/90047655797243760000\) | \(-17208375004676935133429760000\) | \([2]\) | \(154140672\) | \(4.1074\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.di have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.di do not have complex multiplication.Modular form 221760.2.a.di
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
