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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 51600.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.du1 | 51600w4 | \([0, 1, 0, -6495408, -6373780812]\) | \(947094050118111698/20769216075\) | \(664614914400000000\) | \([2]\) | \(1966080\) | \(2.5356\) | |
| 51600.du2 | 51600w2 | \([0, 1, 0, -420408, -92230812]\) | \(513591322675396/68238500625\) | \(1091816010000000000\) | \([2, 2]\) | \(983040\) | \(2.1890\) | |
| 51600.du3 | 51600w1 | \([0, 1, 0, -107908, 12144188]\) | \(34739908901584/4081640625\) | \(16326562500000000\) | \([2]\) | \(491520\) | \(1.8424\) | \(\Gamma_0(N)\)-optimal |
| 51600.du4 | 51600w3 | \([0, 1, 0, 654592, -485680812]\) | \(969360123836302/3748293231075\) | \(-119945383394400000000\) | \([2]\) | \(1966080\) | \(2.5356\) |
Rank
sage: E.rank()
The elliptic curves in class 51600.du have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.du do not have complex multiplication.Modular form 51600.2.a.du
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.
