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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 40656.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.di1 | 40656ba4 | \([0, 1, 0, -77468112, -186113921292]\) | \(14171198121996897746/4077720290568771\) | \(14794609122673259564095488\) | \([4]\) | \(11059200\) | \(3.5361\) | |
| 40656.di2 | 40656ba2 | \([0, 1, 0, -71026072, -230391350620]\) | \(21843440425782779332/3100814593569\) | \(5625120975050435798016\) | \([2, 2]\) | \(5529600\) | \(3.1895\) | |
| 40656.di3 | 40656ba1 | \([0, 1, 0, -71023652, -230407834692]\) | \(87364831012240243408/1760913\) | \(798608587569408\) | \([2]\) | \(2764800\) | \(2.8429\) | \(\Gamma_0(N)\)-optimal |
| 40656.di4 | 40656ba3 | \([0, 1, 0, -64622752, -273613760620]\) | \(-8226100326647904626/4152140742401883\) | \(-15064618200576455166695424\) | \([2]\) | \(11059200\) | \(3.5361\) |
Rank
sage: E.rank()
The elliptic curves in class 40656.di have rank \(0\).
Complex multiplication
The elliptic curves in class 40656.di do not have complex multiplication.Modular form 40656.2.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.
