Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 304920o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304920.o1 | 304920o1 | \([0, 0, 0, -131043, 17965838]\) | \(188183524/3465\) | \(4582334988887040\) | \([2]\) | \(2211840\) | \(1.7997\) | \(\Gamma_0(N)\)-optimal |
| 304920.o2 | 304920o2 | \([0, 0, 0, -363, 52177862]\) | \(-2/444675\) | \(-1176132647147673600\) | \([2]\) | \(4423680\) | \(2.1463\) |
Rank
sage: E.rank()
The elliptic curves in class 304920o have rank \(0\).
Complex multiplication
The elliptic curves in class 304920o do not have complex multiplication.Modular form 304920.2.a.o
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 Cremona 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 Cremona labels.
