Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 90480.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.q1 | 90480bf1 | \([0, -1, 0, -86505, 7428960]\) | \(4474375016012824576/1110767472704565\) | \(17772279563273040\) | \([2]\) | \(599040\) | \(1.8283\) | \(\Gamma_0(N)\)-optimal |
| 90480.q2 | 90480bf2 | \([0, -1, 0, 208740, 46873692]\) | \(3929150857812183344/5992508593577025\) | \(-1534082199955718400\) | \([2]\) | \(1198080\) | \(2.1749\) |
Rank
sage: E.rank()
The elliptic curves in class 90480.q have rank \(0\).
Complex multiplication
The elliptic curves in class 90480.q do not have complex multiplication.Modular form 90480.2.a.q
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.
