Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 6480.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.x1 | 6480z2 | \([0, 0, 0, -32427, -2257254]\) | \(-15590912409/78125\) | \(-18895680000000\) | \([]\) | \(16128\) | \(1.3948\) | |
| 6480.x2 | 6480z1 | \([0, 0, 0, -27, 1674]\) | \(-9/5\) | \(-1209323520\) | \([]\) | \(2304\) | \(0.42186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6480.x have rank \(0\).
Complex multiplication
The elliptic curves in class 6480.x do not have complex multiplication.Modular form 6480.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
