Show commands:
SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 12480.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.cq1 | 12480cy4 | \([0, 1, 0, -76545, 7710975]\) | \(189208196468929/10860320250\) | \(2846967791616000\) | \([2]\) | \(55296\) | \(1.7195\) | |
| 12480.cq2 | 12480cy2 | \([0, 1, 0, -13185, -584577]\) | \(967068262369/4928040\) | \(1291856117760\) | \([2]\) | \(18432\) | \(1.1702\) | |
| 12480.cq3 | 12480cy1 | \([0, 1, 0, -385, -18817]\) | \(-24137569/561600\) | \(-147220070400\) | \([2]\) | \(9216\) | \(0.82366\) | \(\Gamma_0(N)\)-optimal |
| 12480.cq4 | 12480cy3 | \([0, 1, 0, 3455, 494975]\) | \(17394111071/411937500\) | \(-107986944000000\) | \([2]\) | \(27648\) | \(1.3730\) |
Rank
sage: E.rank()
The elliptic curves in class 12480.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 12480.cq do not have complex multiplication.Modular form 12480.2.a.cq
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
