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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 5520.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.a1 | 5520q3 | \([0, -1, 0, -482136, -128644560]\) | \(3026030815665395929/1364501953125\) | \(5589000000000000\) | \([2]\) | \(76800\) | \(1.9794\) | |
| 5520.a2 | 5520q4 | \([0, -1, 0, -265016, 51687216]\) | \(502552788401502649/10024505152875\) | \(41060373106176000\) | \([2]\) | \(76800\) | \(1.9794\) | |
| 5520.a3 | 5520q2 | \([0, -1, 0, -35016, -1304784]\) | \(1159246431432649/488076890625\) | \(1999162944000000\) | \([2, 2]\) | \(38400\) | \(1.6328\) | |
| 5520.a4 | 5520q1 | \([0, -1, 0, 7304, -153680]\) | \(10519294081031/8500170375\) | \(-34816697856000\) | \([2]\) | \(19200\) | \(1.2863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.a have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.a do not have complex multiplication.Modular form 5520.2.a.a
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.
