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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6480.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.c1 | 6480j2 | \([0, 0, 0, -1728, 26352]\) | \(2359296/125\) | \(30233088000\) | \([]\) | \(5184\) | \(0.76782\) | |
| 6480.c2 | 6480j1 | \([0, 0, 0, -288, -1872]\) | \(884736/5\) | \(14929920\) | \([]\) | \(1728\) | \(0.21851\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6480.c have rank \(0\).
Complex multiplication
The elliptic curves in class 6480.c do not have complex multiplication.Modular form 6480.2.a.c
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.
