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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 162288.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.e1 | 162288cz2 | \([0, 0, 0, -16708167, 26269474770]\) | \(870143011569648/671898241\) | \(398311643547370328832\) | \([2]\) | \(11943936\) | \(2.8845\) | |
| 162288.e2 | 162288cz1 | \([0, 0, 0, -825552, 587286315]\) | \(-1679412953088/3049579729\) | \(-112989869583794442288\) | \([2]\) | \(5971968\) | \(2.5379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162288.e have rank \(1\).
Complex multiplication
The elliptic curves in class 162288.e do not have complex multiplication.Modular form 162288.2.a.e
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.
