Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9633.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9633.p1 | 9633p2 | \([0, 1, 1, -741966, -246241771]\) | \(-9358714467168256/22284891\) | \(-107564912442819\) | \([]\) | \(115200\) | \(1.9339\) | |
| 9633.p2 | 9633p1 | \([0, 1, 1, 3324, -83131]\) | \(841232384/1121931\) | \(-5415346648179\) | \([]\) | \(23040\) | \(1.1292\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9633.p have rank \(1\).
Complex multiplication
The elliptic curves in class 9633.p do not have complex multiplication.Modular form 9633.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
