Show commands:
SageMath
E = EllipticCurve("jp1")
E.isogeny_class()
Elliptic curves in class 159936.jp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.jp1 | 159936cb2 | \([0, 1, 0, -737, 5823]\) | \(3944312/867\) | \(9744580608\) | \([2]\) | \(73728\) | \(0.63020\) | |
| 159936.jp2 | 159936cb1 | \([0, 1, 0, 103, 615]\) | \(85184/153\) | \(-214953984\) | \([2]\) | \(36864\) | \(0.28362\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.jp have rank \(0\).
Complex multiplication
The elliptic curves in class 159936.jp do not have complex multiplication.Modular form 159936.2.a.jp
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.
