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SageMath
E = EllipticCurve("mw1")
E.isogeny_class()
Elliptic curves in class 221760.mw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.mw1 | 221760d3 | \([0, 0, 0, -153280812, 730432018384]\) | \(2084105208962185000201/31185000\) | \(5959546306560000\) | \([2]\) | \(18874368\) | \(3.0306\) | |
| 221760.mw2 | 221760d4 | \([0, 0, 0, -10386732, 9377910736]\) | \(648474704552553481/176469171805080\) | \(33723783904206079918080\) | \([2]\) | \(18874368\) | \(3.0306\) | |
| 221760.mw3 | 221760d2 | \([0, 0, 0, -9580332, 11412296656]\) | \(508859562767519881/62240270400\) | \(11894300900484710400\) | \([2, 2]\) | \(9437184\) | \(2.6840\) | |
| 221760.mw4 | 221760d1 | \([0, 0, 0, -548652, 209400784]\) | \(-95575628340361/43812679680\) | \(-8372733473382727680\) | \([2]\) | \(4718592\) | \(2.3374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221760.mw have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.mw do not have complex multiplication.Modular form 221760.2.a.mw
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
