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SageMath
E = EllipticCurve("pb1")
E.isogeny_class()
Elliptic curves in class 187200.pb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.pb1 | 187200od1 | \([0, 0, 0, -3000, 29000]\) | \(256000/117\) | \(1364688000000\) | \([2]\) | \(294912\) | \(1.0234\) | \(\Gamma_0(N)\)-optimal |
| 187200.pb2 | 187200od2 | \([0, 0, 0, 10500, 218000]\) | \(686000/507\) | \(-94618368000000\) | \([2]\) | \(589824\) | \(1.3700\) |
Rank
sage: E.rank()
The elliptic curves in class 187200.pb have rank \(0\).
Complex multiplication
The elliptic curves in class 187200.pb do not have complex multiplication.Modular form 187200.2.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.
