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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5520z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.r2 | 5520z1 | \([0, 1, 0, 2664, 27540]\) | \(510273943271/370215360\) | \(-1516402114560\) | \([2]\) | \(8064\) | \(1.0256\) | \(\Gamma_0(N)\)-optimal |
| 5520.r1 | 5520z2 | \([0, 1, 0, -12056, 221844]\) | \(47316161414809/22001657400\) | \(90118788710400\) | \([2]\) | \(16128\) | \(1.3722\) |
Rank
sage: E.rank()
The elliptic curves in class 5520z have rank \(1\).
Complex multiplication
The elliptic curves in class 5520z do not have complex multiplication.Modular form 5520.2.a.z
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
