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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6480.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.n1 | 6480v2 | \([0, 0, 0, -631827, 193311954]\) | \(-115330920751809/4096000\) | \(-990677827584000\) | \([]\) | \(77760\) | \(1.9669\) | |
| 6480.n2 | 6480v1 | \([0, 0, 0, -1827, 657954]\) | \(-225866529/62500000\) | \(-186624000000000\) | \([]\) | \(25920\) | \(1.4176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6480.n have rank \(1\).
Complex multiplication
The elliptic curves in class 6480.n do not have complex multiplication.Modular form 6480.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
