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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5520.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.e1 | 5520a4 | \([0, -1, 0, -2160176, 1222750176]\) | \(544328872410114151778/14166950625\) | \(29013914880000\) | \([4]\) | \(49152\) | \(2.0986\) | |
| 5520.e2 | 5520a3 | \([0, -1, 0, -209696, -4219680]\) | \(497927680189263938/284271240234375\) | \(582187500000000000\) | \([2]\) | \(49152\) | \(2.0986\) | |
| 5520.e3 | 5520a2 | \([0, -1, 0, -135176, 19090176]\) | \(266763091319403556/1355769140625\) | \(1388307600000000\) | \([2, 2]\) | \(24576\) | \(1.7520\) | |
| 5520.e4 | 5520a1 | \([0, -1, 0, -3956, 614400]\) | \(-26752376766544/618796614375\) | \(-158411933280000\) | \([2]\) | \(12288\) | \(1.4054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.e have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.e do not have complex multiplication.Modular form 5520.2.a.e
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.
