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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 271440.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271440.dj1 | 271440dj4 | \([0, 0, 0, -46951707, -123829390006]\) | \(3833455222908263170009/14910644531250\) | \(44522946000000000000\) | \([2]\) | \(11796480\) | \(2.9833\) | |
| 271440.dj2 | 271440dj2 | \([0, 0, 0, -2978427, -1873895254]\) | \(978581759592931129/58281773062500\) | \(174028441856256000000\) | \([2, 2]\) | \(5898240\) | \(2.6367\) | |
| 271440.dj3 | 271440dj1 | \([0, 0, 0, -556347, 123351914]\) | \(6377838054073849/1489533786000\) | \(4447724052455424000\) | \([2]\) | \(2949120\) | \(2.2901\) | \(\Gamma_0(N)\)-optimal |
| 271440.dj4 | 271440dj3 | \([0, 0, 0, 2241573, -7742219254]\) | \(417152543917888871/8913566138987250\) | \(-26615765873957704704000\) | \([2]\) | \(11796480\) | \(2.9833\) |
Rank
sage: E.rank()
The elliptic curves in class 271440.dj have rank \(0\).
Complex multiplication
The elliptic curves in class 271440.dj do not have complex multiplication.Modular form 271440.2.a.dj
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.
