Show commands:
SageMath
E = EllipticCurve("pb1")
E.isogeny_class()
Elliptic curves in class 235200.pb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.pb1 | 235200pb1 | \([0, 1, 0, -1412833, 625186463]\) | \(5177717/189\) | \(11384658432000000000\) | \([2]\) | \(5898240\) | \(2.4262\) | \(\Gamma_0(N)\)-optimal |
| 235200.pb2 | 235200pb2 | \([0, 1, 0, 547167, 2226506463]\) | \(300763/35721\) | \(-2151700443648000000000\) | \([2]\) | \(11796480\) | \(2.7728\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.pb have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.pb do not have complex multiplication.Modular form 235200.2.a.pb
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.
