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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 5520.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.k1 | 5520d2 | \([0, -1, 0, -518720, -143623200]\) | \(7536914291382802562/17961229575\) | \(36784598169600\) | \([2]\) | \(42240\) | \(1.8444\) | |
| 5520.k2 | 5520d1 | \([0, -1, 0, -32040, -2291328]\) | \(-3552342505518244/179863605135\) | \(-184180331658240\) | \([2]\) | \(21120\) | \(1.4978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.k have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.k do not have complex multiplication.Modular form 5520.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
